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Regularity results for a noncoercive nonlinear Dirichlet problem Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-06-21 Emilia Anna Alfano, Patrizia Di Gironimo, Sara Monsurrò
In this paper, we prove some regularity results for a noncoercive nonlinear Dirichlet problem in an unbounded domain. The main result is obtained in the hypothesis that suitable coefficients of the operator associated to the problem belong to a class of functional spaces strictly containing Lebesgue ones. This can be done by approximation via coercive nonlinear Dirichlet problems. Under additional
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Existence, uniqueness, and approximation of a fictitious domain formulation for fluid-structure interactions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-06-14 Daniele Boffi, Lucia Gastaldi
In this paper, we describe a computational model for the simulation of fluidstructure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the finite element immersed boundary method (FE-IBM) to the actual finite element distributed Lagrange multiplier (FEDLM) method. We recall the well-posedness of our formulation
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Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-06-14 Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels
This paper deals with a general system of equations and conditions arising from a mathematical model of prostate cancer growth with chemotherapy and antiangiogenic therapy that has been recently introduced and analyzed; see P. Colli et al. [Math. Models Methods Appl. Sci. 30 (2020), 1253–1295]. The related system includes two evolutionary operator equations involving fractional powers of selfadjoint
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Integer solutions to bankruptcy problems: The IPROP solution Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-06-10 Vito Fragnelli, Fabio Gastaldi
A widely studied problem is that of a bankruptcy, where several agents claim different amounts of a resource, the estate, that is not enough to satisfy all claims. In some occurrences, the estate is made by integer unities: several contributors (among them also the authors) have proposed different approaches related to some of the classical apportionment rules. In this paper, we analyze the possibility
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The Chern–Ricci flow Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-06-09 Valentino Tosatti, Ben Weinkove
We give a survey on the Chern–Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.
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An uncoupled limit model for a high-contrast problem in a thin multi-structure Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-03-30 Umberto De Maio, Antonio Gaudiello, Ali Sili
We investigate a degenerating elliptic problem in a multi-structure $\Omega_\varepsilon$ of $\mathbb{R}^3$, in the framework of the thermal stationary conduction with highly contrasting diffusivity. Precisely, $\Omega_\varepsilon$ consists of a fixed basis $\Omega^-$ surmounted by a thin cylinder $\Omega_\varepsilon^+$ with height $1$ and cross-section with a small diameter of order $\varepsilon$.
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Some properties of the torsion function with Robin boundary conditions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-03-15 Rossano Sannipoli
In this paper we study some properties of the torsion function with Robin boundary conditions. Here we write the shape derivative of the $L^{\infty}$ and $L^p$ norms, for $p\ge 1$, of the torsion function, seen as a functional on a bounded simply connected open set $\Omega\subset\mathbb{R}^n$, and prove that the balls are critical shapes for these functionals, when the volume of $\Omega$ is preserved
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Betti numbers of Brill–Noether varieties on a general curve Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-03-15 Camilla Felisetti, Claudio Fontanari
We compute the rational cohomology groups of the smooth Brill–Noether varieties $G^r_d(C)$, parametrizing linear series of degree $d$ and dimension exactly $r$ on a general curve $C$. As an application, we determine the whole intersection cohomology of the singular Brill–Noether loci $W^r_d(C)$, parametrizing complete linear series on $C$ of degree $d$ and dimension at least $r$.
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$\Gamma$-Stability of maximal monotone processes Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Augusto Visintin
The flow of noncyclic maximal monotone operators is formulated variationally as null-minimization problems, via results of Brezis, Ekeland, Nayroles and Fitzpatrick. By means of De Giorgi’s theory of $\Gamma$-convergence, the compactness and the stability of these flows are derived under nonparametric perturbations of the operator. These results are here reviewed, and are applied to quasilinear equations
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Algebraic representation of dual scalar products and stabilization of saddle point problems Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Silvia Bertoluzza
We provide a systematic way to design computable bilinear forms which, on the class of subspaces $W \subseteq \mathcal{V}'$ that can be obtained by duality from a given finite dimensional subspace $W$ of an Hilbert space $\mathcal{V}$, are spectrally equivalent to the scalar product of $\mathcal{V}'$. In the spirit of Baiocchi–Brezzi (1993) and Bertoluzza (1998), such bilinear forms can be used to
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Carleson estimates for the singular parabolic $p$-Laplacian in time-dependent domains Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Ugo Gianazza
We deal with the parabolic $p$-Laplacian in the so-called singular super-critical range $\frac{2N}{N+1}
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Elastic-brittle reinforcement of flexural structures Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Francesco Maddalena, Danilo Percivale, Franco Tomarelli
This note provides a variational description of the mechanical effects of flexural stiffening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforcement is assumed to be linear elastic outside possible free plastic yield lines or free crack. Explicit Euler equations and a compliance identity are shown for the reinforcement of a 1D beam.
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Weak topology and Opial property in Wasserstein spaces, with applications to gradient flows and proximal point algorithms of geodesically convex functionals Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Emanuele Naldi, Giuseppe Savaré
In this paper we discuss how to define an appropriate notion of weak topology in the Wasserstein space $(\mathcal{P}_2(\mathsf{H}),W_2)$ of Borel probability measures with finite quadratic moment on a separable Hilbert space $\mathsf{H}$. We will show that such a topology inherits many features of the usual weak topology in Hilbert spaces, in particular the weak closedness of geodesically convex closed
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Closed selections of Vitali’s type Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Jeremy Mirmina, Daniele Puglisi
Assume that $G$ is a group acting on a Polish space. Given a subgroup $H$ of $G$, by a closed $H$-selection we mean a closed selection on each orbit of $H$. We investigate measurability properties of closed $H$-selections with respect to $G$-invariant measures, extending some classical result.
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Equilibria of static systems Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Włodzimierz M. Tulczyjew
A conceptual framework for variational formulations of physical theories is proposed. Such a framework is displayed here just for statics, but it is designed to be subsequently adapted to variational formulations of static field theories and dynamics.
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Non-homogeneous Dirichlet problems with concave-convex reaction Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Gabriele Bonanno, Roberto Livrea, Vicenţiu D. Rădulescu
The variational methods are adopted for establishing the existence of at least two nontrivial solutions for a Dirichlet problem driven by a non-homogeneous differential operator of $p$-Laplacian type. A large class of nonlinear terms is considered, covering the concave-convex case. In particular, two positive solutions to the problem are obtained under a $(p - 1)$-superlinear growth at infinity, provided
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On algebraic values of Weierstrass $\sigma$-functions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-21 Gareth Boxall, Taboka Chalebgwa, Gareth A. Jones
Suppose that $\Omega$ is a lattice in the complex plane and let $\sigma$ be the corresponding Weierstrass $\sigma$-function. Assume that the point $\tau$ associated with $\Omega$ in the standard fundamental domain has imaginary part at most 1.9. Assuming that $\Omega$ has algebraic invariants $g_2,g_3$ we show that a bound of the form $c d^m (\log H)^n$ holds for the number of algebraic points of height
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A multiplicity theorem for anisotropic Robin equations Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2022-02-15 Nikolaos S. Papageorgiou, Patrick Winkert
In this paper, we consider an anisotropic Robin problem driven by the $p(x)$-Laplacian and a superlinear reaction. Applying variational tools along with truncation and comparison techniques as well as critical groups, we prove that the problem has at least five nontrivial smooth solutions to be ordered and with sign information: two positive, two negative, and the fifth nodal.
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Fibonacci expansions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Claudio Baiocchi, Vilmos Komornik, Paola Loreti
Expansions in the Golden ratio base have been studied since a pioneering paper of Rényi more than sixty years ago. We introduce closely related expansions of a new type, based on the Fibonacci sequence, and we show that in some sense they behave better.
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Discontinuous solutions of $U_t + H(U_x) = 0$ versus measure-valued solutions of $u_t + [H(u)]_x = 0$ Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Alberto Tesei
Let $H$ be a bounded Lipschitz continuous function. We discuss some recent results concerning discontinuous viscosity solutions of the Hamilton–Jacobi equation $U_t + H(U_x) = 0$ 0, signed Radon measure-valued entropy solutions of the conservation law $u_t + [H(u)]_x = 0$, and their connection.
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Shape optimization problems in control form Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Giuseppe Buttazzo, Francesco Paolo Maiale, Bozhidar Velichkov
We consider a shape optimization problem written in the optimal control form: the governing operator is the $p$-Laplacian in the Euclidean space $\mathbb{R}^d$, the cost is of an integral type, and the control variable is the domain of the state equation. Conditions that guarantee the existence of an optimal domain will be discussed in various situations. It is proved that the optimal domains have
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A physics-informed multi-fidelity approach for the estimation of differential equations parameters in low-data or large-noise regimes Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Francesco Regazzoni, Stefano Pagani, Alessandro Cosenza, Alessandro Lombardi, Alfio Quarteroni
In this paper, we propose a multi-fidelity approach for parameter estimation problems based on Physics-Informed Neural Networks (PINNs). The proposed methods apply to models expressed by linear or nonlinear differential equations, whose parameters need to be estimated starting from (possibly partial and noisy) measurements of the model’s solution. To overcome the limitations of PINNs in case only few
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On a class of Fokker–Planck equations with subcritical confinement Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Giuseppe Toscani, Mattia Zanella
We study the relaxation to equilibrium for a class of linear one-dimensional Fokker–Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker–Planck equations is that, for any given probability density $e(x)$, the diffusion coefficient can be built to have $e(x)$ as steady state. This representation of the equilibrium density can
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Counting rational points on elliptic curves with a rational 2-torsion point Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Francesco Naccarato
Let $ E/\mathbb{Q}$ be an elliptic curve over the rational numbers. It is known, by the work of Bombieri and Zannier, that if $E$ has full rational 2-torsion, the number $N_E(B)$ of rational points with Weil height bounded by $B$ is $\operatorname{exp}\big(O \big(\frac{\operatorname{log}B}{\sqrt{\operatorname{log}\operatorname{log} B}}\big)\big)$. In this paper we exploit the method of descent via
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Smooth homeomorphic approximation of piecewise affine homeomorphisms Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Daniel Campbell, Filip Soudský
Given any $f$ a locally finitely piecewise affine homeomorphism of $\Omega \subset \mathbb{R}^n$ onto $\Delta \subset \mathbb{R}^n$ in $W^{1,p}, 1 \leq p < \infty$ and any $\varepsilon > 0$ we construct a smooth injective map $\tilde{f}$ such that $\|f-\tilde{f}\|_{W^{1,p}(\Omega,\mathbb{R}^n)} < \varepsilon$.
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Optimal horizontal joinability on the Engel group Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Alexander Greshnov
On the Engel group we solve the problem of finding the minimal number of segments of integral lines of left-invariant basis horizontal vector fields necessary for joining an arbitrary pair of points. We prove the best version of Rashevskii–Chow Theorem on Engel group.
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Evolution by Levi form in $\mathbb{P}^2$ Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Giuseppe Tomassini
In this paper we introduce the notion of evolution by Levi form of a closed set $K$ in the complex projective space $\mathbb{P}^2$, which is governed by a parabolic problem for the Levi operator. The main result of the paper is the following: if $K$ is the closure of a pseudoconvex domain with a regular boundary then the evolution is contained in $K$. As a consequence, a hypothetic Levi flat hypersurface
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Hilbert modules and complex analytic fibre spaces Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Harald Upmeier
We describe the ‘‘eigenbundle’’ (localization bundle) of Hilbert modules over bounded symmetric domains and show that the fibres are closely related to Kähler geometry of certain flag manifolds defined in terms of Jordan algebras. This gives an intriguing relationship between Hilbert space operators, coherent module sheaves and geometry of Jordan manifolds. The resulting complex-analytic fibre spaces
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Multipoint Julia theorems Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-12-16 Marco Abate
Following ideas introduced by Beardon–Minda and by Baribeau–Rivard–Wegert in the context of the Schwarz–Pick lemma, we use the iterated hyperbolic difference quotients to prove a multipoint Julia lemma. As applications, we give a sharp estimate from below of the angular derivative at a boundary point, generalizing results due to Osserman, Mercer and others; and we prove a generalization to multiple
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Sub-shock formation in shock structure of a binary mixture of polyatomic gases Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Tommaso Ruggeri, Shigeru Taniguchi
The differential system of the field equations of a binary mixture of Eulerian gases is hyperbolic and, according to a general theorem of Boillat and Ruggeri, the shock-structure solution is not always regular and a discontinuous jump (sub-shock) may appear depending on the velocity of the shock wave. In this paper, we give all the necessary conditions for the subshock formation and we identify for
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On topologically trivial automorphisms of compact Kähler manifolds and algebraic surfaces Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Fabrizio Catanese, Wenfei Liu
In this paper, we investigate automorphisms of compact Kähler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces $X$ whose groups of $C^\infty$-isotopically trivial automorphisms, resp. cohomologically trivial automorphisms, have a number of connected components which can be arbitrarily large.
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Radon measure-valued solutions of quasilinear parabolic equations Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Alberto Tesei
We discuss some recent results concerning Radon measure-valued solutions of the Cauchy–Dirichlet problem for $\partial_t u = \Delta\phi(u)$. The function $\phi$ is continuous, nondecreasing, with a growth at most powerlike. Well-posedness and regularity results are described, which depend on whether the initial data charge sets of suitable capacity (determined both by the Laplacian and by the growth
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Mathematical and numerical models for the cardiac electromechanical function Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Luca Dedè, Alfio Quarteroni, Francesco Regazzoni
This paper deals with the mathematical model that describes the function of the human heart. More specifically, it addresses the equations that express the electromechanical process, that is the mechanical deformation (contraction and relaxation) of the heart muscle that is induced by the electrical field that, at every heartbeat, is generated in the sino-atrial node and then propagates all across
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Output stabilization of strongly minimum-phase multivariable nonlinear systems Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Alberto Isidori
This paper addresses the problem of output stabilization of invertible MIMO nonlinear systems. A unifying procedure is presented, that consists in the preliminary use of a statefeedback to induce an upper triangular structure. Assuming that the upper subsystem in this structure is input-to-state stable (to a compact invariant set), the output stabilization problem is reduced to the problem of globally
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Kinetic SIR equations and particle limits Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Alessandro Ciallella, Mario Pulvirenti, Sergio Simonella
We present and analyze two simple $N$-particle systems for the spread of an infection, respectively with binary and with multi-body interactions. We establish a convergence result, as $N\to\infty$, to a set of kinetic equations, providing a mathematical justification of related numerical schemes. We analyze rigorously the time asymptotics of these equations, and compare the models numerically.
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Morrey estimates for a class of noncoercive elliptic systems with VMO-coefficients Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Giuseppa Rita Cirmi, Salvatore D’Asero, Salvatore Leonardi
We consider a non-coercive vectorial boundary value problem with non smooth coefficients and a drift term and we study the regularity of a solution $u$ and its gradient in the framework of suitable Morrey spaces.
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Interacting particle systems with long-range interactions: scaling limits and kinetic equations Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-07-14 Alessia Nota, Juan J.L. Velázquez, Raphael Winter
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation
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A differential algebra and the homotopy type of the complement of a toric arrangement Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Corrado De Concini, Giovanni Gaiffi
We show that the rational homotopy type of the complement of a toric arrangement is completely determined by two sets of discrete data. This is obtained by introducing a differential graded algebra over Q whose minimal model is equivalent to the Sullivan minimal model of $\mathcal A$.
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Norms and Cayley–Hamilton algebras Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Claudio Procesi
We develop the general Theory of Cayley–Hamilton algebras using norms and compare with the approach, valid only in characteristic 0, using traces and presented in a previous paper [19].
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On the infinitesimal Terracini Lemma Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Ciro Ciliberto
In this paper we prove an infinitesimal version of the classical Terracini Lemma for 3-secant planes to a variety. Precisely we prove that if $X \subseteq \mathcal P'$ is an irreducible, non-degenerate, projective complex variety of dimension $n$ with $r \geq 3n + 2$, such that the variety of osculating planes to curves in $X$ has the expected dimension $3n$ and for every 0-dimensional, curvilinear
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On the Schwartz correspondence for Gelfand pairs of polynomial growth Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Francesca Astengo, Bianca Di Blasio, Fulvio Ricci
Let $(G,K)$ be a Gelfand pair, with $G$ a Lie group of polynomial growth, and let $\Sigma\subset\mathbb R^\ell$ be a homeomorphic image of the Gelfand spectrum, obtained by choosing a generating system $D_1,\dots,D_\ell$ of $G$-invariant differential operators on $G/K$ and associating to a bounded spherical function $\phi$ the $\ell$-tuple of its eigenvalues under the action of the $D_j$'s. We say
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$\Gamma$-convergence for a class of action functionals induced by gradients of convex functions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Luigi Ambrosio, Aymeric Baradat, Yann Brenier
Given a real function $f$, the rate function for the large deviations of the diffusion process of drift $\nabla f$ given by the Freidlin–Wentzell theorem coincides with the time integral of the energy dissipation for the gradient flow associated with $f$. This paper is concerned with the stability in the hilbertian framework of this common action functional when $f$ varies. More precisely, we show
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Uniqueness theory for model sets, and spectral superresolution Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 John J. Benedetto, Chenzhi Zhao
We build on the work of Basarab Matei by proving a new uniqueness theorem for some complex Radon measures whose Fourier transforms vanish on the model sets formulated by Yves Meyer. Although apparently specialized, it fits naturally into the broad areas of the extension problem for positive definite functions, spectral estimation, and spectral super-resolution. Out technology involves Kronecker’s theorem
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Contracting properties of bounded holomorphic functions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Manabu Ito
The classical Schwarz–Pick lemma implies that a holomorphic function of the open unit disk into itself gives a contraction with respect to the hyperbolic metric on the disk. In this article, we formulate a more general contracting property of a bounded holomorphic function in settings with respect to a conformal semimetric. During the study, it will become clear that a proper holomorphic mapping plays
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Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-04-22 Filippo Giuliani, Marcel Guardia, Pau Martin, Stefano Pasquali
The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on T2 exchanging energy among Fourier modes in a "chaotic-like" way. We say that a transition of energy is "chaotic-like" if either the choice of activated modes or the time spent in each transfer can be chosen randomly. We consider the nonlinear cubic Wave, the
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A note on the zeroes of the Fredholm series Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Umberto Zannier
The issue had been raised whether the function $z + z^2 + \cdots + z^{2n}, sometimes called Fredholm series, has infinitely many zeroes in the unit disk. We provide an affirmative answer, proving that in fact every complex number occurs as a value infinitely many times, even restricting the function to any open set meeting the unit circle.
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Positive solution to Schrödinger equation with singular potential and double critical exponents Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Yu Su
In this paper, we consider the following Schrödinger equation with singular potential and double critical exponents: $$-\Delta u + \frac{A}{|x|^{\alpha}}u = |u|^{2^{*}-2}u + |u|^{p-2}u + \lambda |u|^{2_{\alpha}^{*}-2}u,\quad x\in \mathbb{R}^{N},$$ where $N\geq 3$, $\alpha\in(0,2)$, $p\in(\frac{2N-4+2\alpha}{N-2},2^{*})$, and $A,\lambda>0$ are two real constants, and $2^{*}=\frac{2N}{N-2}$ is the Sobolev
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Totally $T$-adic functions of small height Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Xander Faber, Clayton Petsche
Let $\mathbb F_q (T)$ be the field of rational functions in one variable over a finite field. We introduce the notion of a totally $T$-adic function: one that is algebraic over $\mathbb F_q (T)$ and whose minimal polynomial splits completely over the completion $\mathbb F_q ((T))$. We give two proofs that the height of a nonconstant totally $T$-adic function is bounded away from zero, each of which
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Homogenization of the backward-forward mean-field games systems in periodic environments Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Pierre-Louis Lions, Panagiotis E. Souganidis
We study the homogenization properties in the small viscosity limit and in periodic environments of the (viscous) backward-forward mean-field games system. We consider separated Hamiltonians and provide results for systems with (i) ‘‘smoothing’’ coupling and general initial and terminal data, and (ii) with ‘‘local coupling’’ but well-prepared data. The limit is a first-order forward-backward system
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Global Lipschitz extension preserving local constants Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Simone Di Marino, Nicola Gigli, Aldo Pratelli
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results to give a simple and direct proof of the fact that Sobolev spaces on metric measure spaces defined with a relaxation approach à la Cheeger are invariant under isomorphism class of mm-structures.
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Higher differentiability for a class of obstacle problems with nearly linear growth conditions Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Chiara Gavioli
We establish higher differentiability results of integer order for solutions to a class of obstacle problems with nearly linear growth, provided that we assume a suitable extra integer differentiability property of Sobolev order on the gradient of the obstacle. Our results cover a large class of models for which the Lavrentiev phenomenon does not appear.
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Weighted strong laws of large numbers on variable exponent vector-valued Lebesgue spaces Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Farrukh Mukhamedov, Humberto Rafeiro
We obtain weighted strong law of large numbers for a sequence of random variables belonging to variable exponent vector-valued Lebesgue spaces. As an application, we establish sufficient conditions for the convergence of weighted ergodic averages and weighted series of contractions in Banach spaces.
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Hilbert-type inequalities in homogeneous cones Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Gustavo Garrigós, Cyrille Nana
We prove $L^p-L^q$ bounds for the class of Hilbert-type operators associated with generalized powers $Q^a$ in a homogeneous cone $\Omega$. Our results extend and slightly improve earlier work from [16], where the problem was considered for scalar powers $\mathbf a = (\alpha, \dots, \alpha)$ and symmetric cones. We give a more transparent proof, provide new examples, and briefly discuss the open question
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Effective cycles on the symmetric product of a curve, II: the Abel–Jacobi faces Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Francesco Bastianelli, Alexis Kouvidakis, Angelo Felice Lopez, Filippo Viviani
In this paper, which is a sequel of [BKLV17], we study the convex-geometric properties of the cone of pseudoeffective $n$-cycles in the symmetric product $C_d$ of a smooth curve $C$. We introduce and study the Abel–Jacobi faces, related to the contractibility properties of the Abel–Jacobi morphism and to classical Brill–Noether varieties. We investigate when Abel–Jacobi faces are non-trivial, and we
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On the limit as $s \to 1^-$ of possibly non-separable fractional Orlicz–Sobolev spaces Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková
Extended versions of the Bourgain–Brezis–Mironescu theorems on the limit as $s \to 1^-$ of the Gagliardo–Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz–Sobolev spaces built upon general Young functions, and complement those of [13], where Young functions satisfying the $\Delta_2$ and the $\nabla_2$ conditions are dealt with. The case
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Time quasi-periodic traveling gravity water waves in infinite depth Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Roberto Feola, Filippo Giuliani
We present the recent result [9] concerning the existence of quasi-periodic in time traveling waves for the $2d$ pure gravity water waves system in infinite depth. We provide the first existence result of quasi-periodic water waves solutions bifurcating from a completely resonant elliptic fixed point. The proof is based on a Nash–Moser scheme, Birkhoff normal form methods and pseudo-differential calculus
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Modeling of a gas slug rising in a cylindrical duct and possible applications to volcanic scenarios Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Angiolo Farina, Jacopo Matrone, Chiara P. Montagna, Fabio Rosso
The paper deals with the mathematical modelling of a gas slug rising in a cylindrical duct filled with an incompressible liquid. This research is motivated by a phenomenon commonly observed during Strombolian eruptions at basaltic volcanoes, that is, mildly explosive events driven by a large bubble of magmatic gas (a slug) rising up the conduit and bursting at the surface. The model is compared with
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Pathology of essential spectra of elliptic problems in periodic family of beads threaded by a spoke thinning at infinity Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Sergei A. Nazarov, Jari Taskinen
We construct ‘‘almost periodic’’ unbounded domains, where a large class of elliptic spectral problems have essential spectra possessing peculiar structure: they consist of monotone, non-negative sequences of isolated points and thus have infinitely many gaps.
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An $\varepsilon$-regularity result for optimal transport maps between continuous densities Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Michael Goldman
The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.
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A note on the construction of Sobolev almost periodic invariant tori for the 1d NLS Rend. Lincei Mat. Appl. (IF 0.5) Pub Date : 2021-02-15 Luca Biasco, Jessica Elisa Massetti, Michela Procesi
We announce a method for the construction of almost periodic solutions of the one dimensional analytic NLS with only Sobolev regularity both in time and space. This is the first result of this kind for PDEs.