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The $$H^\infty $$ -Functional Calculi for the Quaternionic Fine Structures of Dirac Type Milan J. Math. (IF 1.7) Pub Date : 2024-03-06 Fabrizio Colombo, Stefano Pinton, Peter Schlosser
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On the Automorphism Groups of Certain Branched Structures on Surfaces Milan J. Math. (IF 1.7) Pub Date : 2024-02-14
Abstract We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving the maximal possible number of automorphisms allowed by their genus and we finally extend the same results to branched projective structures.
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Leray–Lions Equations of (p, q)-Type in the Entire Space with Unbounded Potentials Milan J. Math. (IF 1.7) Pub Date : 2024-02-11 Federica Mennuni, Dimitri Mugnai
In this paper we prove the existence of signed bounded solutions for a quasilinear elliptic equation in \({\mathbb {R}}^N\) driven by a Leray–Lions operator of (p, q)–type in presence of unbounded potentials. A direct approach seems to be a hard task, and for this reason we will study approximating problems in bounded domains, whose resolutions needs refined tools from nonlinear analysis. In particular
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Deficiency Indices for Singular Magnetic Schrödinger Operators Milan J. Math. (IF 1.7) Pub Date : 2024-01-08 Michele Correggi, Davide Fermi
We show that the deficiency indices of magnetic Schrödinger operators with several local singularities can be computed in terms of the deficiency indices of operators carrying just one singularity each. We discuss some applications to physically relevant operators.
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Another Look at Elliptic Homogenization Milan J. Math. (IF 1.7) Pub Date : 2023-12-03 Andrea Braides, Giuseppe Cosma Brusca, Davide Donati
We consider the limit of sequences of normalized (s, 2)-Gagliardo seminorms with an oscillating coefficient as \(s\rightarrow 1\). In a seminal paper by Bourgain et al. (Another look at Sobolev spaces. In: Optimal control and partial differential equations. IOS, Amsterdam, pp 439–455, 2001) it is proven that if the coefficient is constant then this sequence \(\Gamma \)-converges to a multiple of the
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On the Dynamics of Aeolian Sand Ripples Milan J. Math. (IF 1.7) Pub Date : 2023-10-26 Giuseppe Maria Coclite, Lorenzo di Ruvo
The dynamics of aeolian sand ripples is described by a 1D non-linear evolutive fourth order equation. In this paper, we prove the well-posedness of the classical solutions of the Cauchy problem, associated with this equation.
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Klein–Gordon–Maxwell Equations Driven by Mixed Local–Nonlocal Operators Milan J. Math. (IF 1.7) Pub Date : 2023-09-07 Nicolò Cangiotti, Maicol Caponi, Alberto Maione, Enzo Vitillaro
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Dynamic Crack Growth in Viscoelastic Materials with Memory Milan J. Math. (IF 1.7) Pub Date : 2023-07-31 Federico Cianci
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Indefinite Perturbations of the Eigenvalue Problem for the Nonautonomous p-Laplacian Milan J. Math. (IF 1.7) Pub Date : 2023-07-27 Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Xueying Sun
We consider an indefinite perturbation of the eigenvalue problem for the nonautonomous p-Laplacian. The main result establishes an exhaustive analysis in the nontrivial case that corresponds to noncoercive perturbations of the reaction. Using variational tools and truncation and comparison techniques, we prove an existence and multiplicity theorem which is global in the parameter. The main result of
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The Third Cohomology 2-Group Milan J. Math. (IF 1.7) Pub Date : 2023-07-19 Alan S. Cigoli, Sandra Mantovani, Giuseppe Metere
In this paper we show that a finite product preserving opfibration can be factorized through an opfibration with the same property, but with groupoidal fibres. If moreover the codomain is additive, one can endow each fibre of the new opfibration with a canonical symmetric 2-group structure. We then apply such factorization to the opfibration that sends a crossed extension of a group C to its corresponding
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$${\mathcal {A}}$$ -Variational Principles Milan J. Math. (IF 1.7) Pub Date : 2023-07-06 Luís Bandeira, Pablo Pedregal
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The Expected Markov Property for Quantum Markov Fields Milan J. Math. (IF 1.7) Pub Date : 2023-05-24 Luigi Accardi, Ameur Dhahri
After a short introduction to the Algebraic formulation of classical stochastic processes and fields, we extend to the quantum case the notion of expected classical Markov field and we prove the equivalence of several formulations of the multi-dimensional Markov property. To this goal we need a Kadison–Schwarz inequality for completely positive maps on \(*\)-algebras which is proved in the appendix
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Root Numbers of 5-adic Curves of Genus Two Having Maximal Ramification Milan J. Math. (IF 1.7) Pub Date : 2023-05-15 Lukas Melninkas
The formulas for local root numbers of abelian varieties of dimension one are known. In this paper we treat the simplest unknown case in dimension two by considering a curve of genus 2 defined over a 5-adic field such that the inertia acts on the first \(\ell \)-adic cohomology group through the largest possible finite quotient, isomorphic to \(C_5\rtimes C_8\). We give a few criteria to identify such
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Extremal Regions and Multiplicity of Positive Solutions for Singular Superlinear Elliptic Systems with Indefinite-Sign Potential Milan J. Math. (IF 1.7) Pub Date : 2023-04-29 Ricardo Lima Alves, Carlos Alberto Santos, Kaye Silva
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Mean-Field Limits for Entropic Multi-Population Dynamical Systems Milan J. Math. (IF 1.7) Pub Date : 2023-04-24 Stefano Almi, Claudio D’Eramo, Marco Morandotti, Francesco Solombrino
The well-posedness of a multi-population dynamical system with an entropy regularization and its convergence to a suitable mean-field approximation are proved, under a general set of assumptions. Under further assumptions on the evolution of the labels, the case of different time scales between the agents’ locations and labels dynamics is considered. The limit system couples a mean-field-type evolution
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On the Stability of Solitons for the Maxwell-Lorentz Equations with Rotating Particle Milan J. Math. (IF 1.7) Pub Date : 2023-03-20 A. I. Komech, E. A. Kopylova
We prove the stability of solitons of the Maxwell–Lorentz equations with extended charged rotating particle. The solitons are solutions which correspond to the uniform rotation of the particle. To prove the stability, we construct the Hamilton–Poisson representation of the Maxwell–Lorentz system. The construction relies on the Hamilton least action principle. The constructed structure is degenerate
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Transfer of Energy from Flexural to Torsional Modes for the Fish-Bone Suspension Bridge Model Milan J. Math. (IF 1.7) Pub Date : 2023-02-18 Clelia Marchionna, Stefano Panizzi
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Cauchy–de Branges Spaces, Geometry of Their Reproducing Kernels and Multiplication Operators Milan J. Math. (IF 1.7) Pub Date : 2023-02-17 Anton Baranov
Cauchy–de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges theory. We consider extensions of two important properties of de Branges spaces to this, more general, setting. First, we discuss geometric properties (completeness, Riesz bases) of systems of reproducing kernels corresponding
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Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class Milan J. Math. (IF 1.7) Pub Date : 2023-02-03 Ratan Kr. Giri, Yehuda Pinchover
Using Harnack’s inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point \(\zeta \in \partial \Omega \cup \{\infty \}\) for the quasilinear elliptic equation $$\begin{aligned} -\text {div}(|\nabla u|_A^{p-2}A\nabla u)+V|u|^{p-2}u =0\quad \text { in } \Omega , \end{aligned}$$ where \(\Omega \) is a domain in
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“Bubbling” and Topological Degeneration in the Calculus of Variations Milan J. Math. (IF 1.7) Pub Date : 2023-01-06 Michael Struwe
After recalling first instances of “topological degeneration” and “bubbling” in geometric analysis we present current challenges in applications of variational methods to problems in this field.
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Stable and Historic Behavior in Replicator Equations Generated by Similar-Order Preserving Mappings Milan J. Math. (IF 1.7) Pub Date : 2022-12-31 Mansoor Saburov
One could observe drastically different dynamics of zero-sum and non-zero-sum games under replicator equations. In zero-sum games, heteroclinic cycles naturally occur whenever the species of the population supersede each other in cyclic fashion (like for the Rock-Paper-Scissors game). In this case, the highly erratic oscillations may cause the divergence of the time averages. In contrast, it is a common
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Prescribing Morse Scalar Curvatures Milan J. Math. (IF 1.7) Pub Date : 2022-12-22 Andrea Malchiodi
In this paper we survey some results on the classical Kazdan–Warner problem, consisting in the conformal prescription of the scalar curvature of a Riemannian manifold. We show how the existence problem can be attacked using a combination of different techniques involving variational theory, asymptotic analysis and Morse-theoretical tools.
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Hyper-Kähler Manifolds Milan J. Math. (IF 1.7) Pub Date : 2022-11-14 Olivier Debarre
The aim of this introductory survey is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyper-Kähler manifolds. These manifolds are interesting from several points of view: dynamical (some have interesting automorphism groups), arithmetical (although we will not say anything on this aspect of the theory), and geometric. It
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Elastoplastic Deformations of Layered Structures Milan J. Math. (IF 1.7) Pub Date : 2022-10-29 Daria Drozdenko, Michal Knapek, Martin Kružík, Kristián Máthis, Karel Švadlenka, Jan Valdman
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On the Hodge and Betti Numbers of Hyper-Kähler Manifolds Milan J. Math. (IF 1.7) Pub Date : 2022-10-29 Pietro Beri, Olivier Debarre
In this survey article, we review past results (obtained by Hirzebruch, Libgober–Wood, Salamon, Gritsenko, and Guan) on Hodge and Betti numbers of Kähler manifolds, and more specifically of hyper-Kähler manifolds, culminating in the bounds obtained by Guan in 2001 on the Betti numbers of hyper-Kähler fourfolds. Let X be a compact Kähler manifold of dimension m. One consequence of the Hirzebruch–Riemann–Roch
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Hyper–Kähler Manifolds of Generalized Kummer Type and the Kuga–Satake Correspondence Milan J. Math. (IF 1.7) Pub Date : 2022-10-19 M. Varesco, C. Voisin
We first describe the construction of the Kuga–Satake variety associated to a (polarized) weight-two Hodge structure of hyper-Kähler type. We describe the classical cases where the Kuga–Satake correspondence between a hyper-Kähler manifold and its Kuga–Satake variety has been proved to be algebraic. We then turn to recent work of O’Grady and Markman which we combine to prove that the Kuga–Satake correspondence
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The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem Milan J. Math. (IF 1.7) Pub Date : 2022-10-03 Alessio Bottini
In these notes we review some basic facts about the LLV Lie algebra. It is a rational Lie algebra, introduced by Looijenga–Lunts and Verbitsky, acting on the rational cohomology of a compact Kähler manifold. We study its structure and describe one irreducible component of the rational cohomology in the case of a compact hyperkähler manifold.
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Multiplicity of Solutions for an Elliptic Kirchhoff Equation Milan J. Math. (IF 1.7) Pub Date : 2022-09-27 David Arcoya, José Carmona, Pedro J. Martínez-Aparicio
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The LLV Decomposition of Hyperkähler Cohomology and Applications to the Nagai Conjecture (After Green–Kim–Laza–Robles) Milan J. Math. (IF 1.7) Pub Date : 2022-09-17 Georg Oberdieck, Jieao Song
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Improvements and Generalizations of Two Hardy Type Inequalities and Their Applications to the Rellich Type Inequalities Milan J. Math. (IF 1.7) Pub Date : 2022-09-15 Megumi Sano
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with best constants. Besides, we improve two Rellich type inequalities by using the improved Hardy type inequality.
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An Improved Setting for Generalized Functions: Fine Ultrafunctions Milan J. Math. (IF 1.7) Pub Date : 2022-07-16 Vieri Benci
Ultrafunctions are a particular class of functions defined on a Non Archimedean field \({\mathbb {E}}\supset {\mathbb {R}}\). They have been introduced and studied in some previous works (Benci, in Adv Nonlinear Stud 13:461–486, 2013; Benci and Luperi Baglini, in Electron J Differ Equ Conf 21:11–21, 2014; Benci et al., in Adv Nonlinear Anal 10. https://doi.org/10.1515/anona-2017-0225.2; Benci et al
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A Global Minimization Trick to Solve Some Classes of Berestycki–Lions Type Problems Milan J. Math. (IF 1.7) Pub Date : 2022-07-07 Claudianor O. Alves
In this paper we show an abstract theorem that can be used to prove the existence of solution for a class of elliptic equation considered in Berestycki–Lions (Arch Ration Mech Anal 82:313–345, 1983) and related problems. Moreover, we use the abstract theorem to show that a class of zero mass problems has multiple solutions, which is a novelty for this type of problem.
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Positive Solutions for a Class of Fractional Choquard Equation in Exterior Domain Milan J. Math. (IF 1.7) Pub Date : 2022-07-06 César T. Ledesma, Olimpio H. Miyagaki
This work concerns with the existence of positive solutions for the following class of fractional elliptic problems, $$\begin{aligned} \left\{ \begin{aligned}&(-\Delta )^{s}u + u = \left( \int _{\Omega } \frac{|u(y)|^p}{|x-y|^{N-\alpha }}dy \right) |u|^{p-2}u,\quad \text{ in } \Omega \\&u=0, \quad {\mathbb {R}}^N {\setminus } \Omega \end{aligned} \right. \end{aligned}$$(0.1) where \(s\in (0,1)\), \(N>
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Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra Milan J. Math. (IF 1.7) Pub Date : 2022-06-21 T. Beckmann
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Riemann and His Time Milan J. Math. (IF 1.7) Pub Date : 2022-06-20 Claudio Procesi
This is an extended version of a lecture given in Varese on 23/09/2021 in occasion of the awarding of the Riemann prize to Terence Tao.
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Effectivity of Semi-positive Line Bundles Milan J. Math. (IF 1.7) Pub Date : 2022-06-11 F. Anella, D. Huybrechts
We review work by Campana–Oguiso–Peternell (J Differ Geom 85(3):397–424, 2010) and Verbitsky (Geom Funct Anal 19(5):1481–1493, 2010) showing that a semi-positive line bundle on a hyperkähler manifold admits at least one non-trivial section. This is modest but tangible evidence towards the SYZ conjecture for hyperkähler manifolds.
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The Decoherence-Free Subalgebra of Gaussian Quantum Markov Semigroups Milan J. Math. (IF 1.7) Pub Date : 2022-06-03 Julián Agredo, Franco Fagnola, Damiano Poletti
We demonstrate a method for finding the decoherence-free subalgebra \({\mathcal {N}}({\mathcal {T}})\) of a Gaussian quantum Markov semigroup on the von Neumann algebra \({\mathcal {B}}(\Gamma (\mathbb {C}^d))\) of all bounded operator on the Fock space \(\Gamma (\mathbb {C}^d)\) on \(\mathbb {C}^d\). We show that \({\mathcal {N}}({\mathcal {T}})\) is a type I von Neumann algebra \(L^\infty (\mathbb
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A Characterization of the Vector Lattice of Measurable Functions Milan J. Math. (IF 1.7) Pub Date : 2022-05-21 Simone Cerreia-Vioglio, Paolo Leonetti, Fabio Maccheroni
Given a probability measure space \((X,\Sigma ,\mu )\), it is well known that the Riesz space \(L^0(\mu )\) of equivalence classes of measurable functions \(f: X \rightarrow \mathbf {R}\) is universally complete and the constant function \(\varvec{1}\) is a weak order unit. Moreover, the linear functional \(L^\infty (\mu )\rightarrow \mathbf {R}\) defined by \(f \mapsto \int f\,\mathrm {d}\mu \) is
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Positive Solutions for Slightly Subcritical Elliptic Problems Via Orlicz Spaces Milan J. Math. (IF 1.7) Pub Date : 2022-04-25 Mabel Cuesta, Rosa Pardo
This paper concerns semilinear elliptic equations involving sign-changing weight function and a nonlinearity of subcritical nature understood in a generalized sense. Using an Orlicz–Sobolev space setting, we consider superlinear nonlinearities which do not have a polynomial growth, and state sufficient conditions guaranteeing the Palais–Smale condition. We study the existence of a bifurcated branch
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Infinitesimal Variation Functions for Families of Smooth Varieties Milan J. Math. (IF 1.7) Pub Date : 2022-04-25 Filippo Francesco Favale, Gian Pietro Pirola
In this paper we introduce some variation functions associated to the rank of the Infinitesimal Variations of Hodge Structure for a family of smooth projective complex curves. We give some bounds and inequalities and, in particular, we prove that if X is a smooth plane curve, then, there exists a first order deformation \(\xi \in H^1(T_X)\) which deforms X as plane curve and such that \(\xi \cdot :H^0(\omega
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One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities Milan J. Math. (IF 1.7) Pub Date : 2022-03-28 Giulia Furioli, Ada Pulvirenti, Elide Terraneo, Giuseppe Toscani
We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic problems, and one-dimensional functional inequalities of the type of Poincaré, Wirtinger and logarithmic Sobolev, with weight, for probability densities with polynomial tails. As main examples, we consider inequalities satisfied by inverse Gamma densities
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Tilings with Nonflat Squares: A Characterization Milan J. Math. (IF 1.7) Pub Date : 2022-03-24 Manuel Friedrich, Manuel Seitz, Ulisse Stefanelli
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual orientations of the squares and that these patterns are periodic and one-dimensional. In contrast to the flat case, the nonflatness of the tiles gives rise to nontrivial
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Time-Space Fractional Diffusion Problems: Existence, Decay Estimates and Blow-Up of Solutions Milan J. Math. (IF 1.7) Pub Date : 2022-03-22 Ruixin Shen, Mingqi Xiang, Vicenţiu D. Rădulescu
The aim of this paper is to study the following time-space fractional diffusion problem $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle \partial _t^\beta u+(-\Delta )^\alpha u+(-\Delta )^\alpha \partial _t^\beta u=\lambda f(x,u) +g(x,t) &{}\text{ in } \Omega \times {\mathbb {R}}^{+},\\ u(x,t)=0\ \ &{}\text{ in } ({\mathbb {R}}^N{\setminus }\Omega )\times {\mathbb {R}}^+,\\ u(x,0)=u_0(x)\
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Lagrangian Fibrations Milan J. Math. (IF 1.7) Pub Date : 2022-03-19 D. Huybrechts, M. Mauri
We review the theory of Lagrangian fibrations of hyperkähler manifolds as initiated by Matsushita. We also discuss more recent work of Shen–Yin and Harder–Li–Shen–Yin. Occasionally, we give alternative arguments and complement the discussion by additional observations.
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On a Solution of the Multidimensional Truncated Matrix-Valued Moment Problem Milan J. Math. (IF 1.7) Pub Date : 2022-03-19 David P. Kimsey, Matina Trachana
We will consider the multidimensional truncated \(p \times p\) Hermitian matrix-valued moment problem. We will prove a characterisation of truncated \(p \times p\) Hermitian matrix-valued multisequence with a minimal positive semidefinite matrix-valued representing measure via the existence of a flat extension, i.e., a rank preserving extension of a multivariate Hankel matrix (built from the given
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Regularity of Normal Forms on Parameters Milan J. Math. (IF 1.7) Pub Date : 2022-01-16 Luis Barreira, Claudia Valls
For nonautonomous differential equations depending on a parameter, we show that the normal form inherits the regularity on the parameter of the original equation, provided that the nonresonances allow a certain spectral gap.
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An Existence Result for a Class of Magnetic Problems in Exterior Domains Milan J. Math. (IF 1.7) Pub Date : 2021-12-07 Claudianor O. Alves, Vincenzo Ambrosio, César E. Torres Ledesma
In this paper we deal with the existence of solutions for the following class of magnetic semilinear Schrödinger equation $$\begin{aligned} (P) \qquad \qquad \left\{ \begin{aligned}&(-i\nabla + A(x))^2u +u = |u|^{p-2}u,\;\;\text{ in }\;\;\Omega ,\\&u=0\;\;\text{ on }\;\;\partial \Omega , \end{aligned} \right. \end{aligned}$$ where \(N \ge 3\), \(\Omega \subset {\mathbb {R}}^N\) is an exterior domain
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Quasistatic Limit of a Dynamic Viscoelastic Model with Memory Milan J. Math. (IF 1.7) Pub Date : 2021-11-30 Gianni Dal Maso, Francesco Sapio
We study the behaviour of the solutions to a dynamic evolution problem for a viscoelastic model with long memory, when the rate of change of the data tends to zero. We prove that a suitably rescaled version of the solutions converges to the solution of the corresponding stationary problem.
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Geometric Methods in Partial Differential Equations Milan J. Math. (IF 1.7) Pub Date : 2021-11-22 Ahmed Sebbar, Daniele Struppa, Oumar Wone
We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of those differential equations. This brings to the center of the analysis several classical results from algebraic geometry, including the Cayley-Bacharach theorem
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Projective Properties of Divergence-Free Symmetric Tensors, and New Dispersive Estimates in Gas Dynamics Milan J. Math. (IF 1.7) Pub Date : 2021-11-20 Denis Serre
The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lie’s group analysis of Newtonian dynamics. When applied to models of gas dynamics—such as Euler system or Boltzmann equation,—in combination with Compensated Integrability
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Second Order Regularity for a Linear Elliptic System Having BMO Coefficients Milan J. Math. (IF 1.7) Pub Date : 2021-11-16 Moscariello, Gioconda, Pascale, Giulio
We consider linear elliptic systems whose prototype is $$\begin{aligned} div \, \Lambda \left[ \,\exp (-|x|) - \log |x|\,\right] I \, Du = div \, F + g \text { in}\, B. \end{aligned}$$(0.1) Here B denotes the unit ball of \(\mathbb {R}^n\), for \(n > 2\), centered in the origin, I is the identity matrix, F is a matrix in \(W^{1, 2}(B, \mathbb {R}^{n \times n})\), g is a vector in \(L^2(B, \mathbb {R}^n)\)
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Relative Subanalytic Sheaves II Milan J. Math. (IF 1.7) Pub Date : 2021-11-05 Monteiro Fernandes, Teresa, Prelli, Luca
We give a new construction of sheaves on a relative site associated to a product \(X \times S\) where S plays the role of a parameter space, expanding the previous construction by the same authors, where the subanalytic structure on S was required. Here we let this last condition fall. In this way the construction becomes much easier to apply when the dimension of S is bigger than one. We also study
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Functional Inequalities: Nonlinear Flows and Entropy Methods as a Tool for Obtaining Sharp and Constructive Results Milan J. Math. (IF 1.7) Pub Date : 2021-10-25 Dolbeault, Jean
Interpolation inequalities play an essential role in analysis with fundamental consequences in mathematical physics, nonlinear partial differential equations (PDEs), Markov processes, etc., and have a wide range of applications in various other areas of Science. Research interests have evolved over the years: while mathematicians were originally focussed on abstract properties (for instance appropriate
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Deformations of Varieties of General Type Milan J. Math. (IF 1.7) Pub Date : 2021-10-16 Kollár, János
We prove that small deformations of a projective variety of general type are also projective varieties of general type, with the same plurigenera.
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Waves in Flexural Beams with Nonlinear Adhesive Interaction Milan J. Math. (IF 1.7) Pub Date : 2021-10-03 Coclite, G. M., Devillanova, G., Maddalena, F.
The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon of attachment-detachment of the beam occurring in adhesion phenomena. We prove existence of solutions in energy space and exhibit various counterexamples to uniqueness
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Asymptotic Properties of Solutions to the Cauchy Problem for Degenerate Parabolic Equations with Inhomogeneous Density on Manifolds Milan J. Math. (IF 1.7) Pub Date : 2021-09-21 Andreucci, Daniele, Tedeev, Anatoli F.
We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending on the behavior of the density function at infinity and the geometry of the manifold, which is described in terms of its isoperimetric function. We establish for
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Ground State Solutions for a Nonlocal Equation in $$\mathbb {R}^2$$ R 2 Involving Vanishing Potentials and Exponential Critical Growth Milan J. Math. (IF 1.7) Pub Date : 2021-08-04 Albuquerque, Francisco S. B., Ferreira, Marcelo C., Severo, Uberlandio B.
In this paper, we study the following class of nonlinear equations: $$\begin{aligned} -\Delta u+V(x) u = \left[ |x|^{-\mu }*(Q(x)F(u))\right] Q(x)f(u),\quad x\in \mathbb {R}^2, \end{aligned}$$ where V and Q are continuous potentials, which can be unbounded or vanishing at infintiy, f(s) is a continuous function, F(s) is the primitive of f(s), \(*\) is the convolution operation and \(0<\mu <2\). Assuming
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Heegner Points and Exceptional Zeros of Garrett p-Adic L-Functions Milan J. Math. (IF 1.7) Pub Date : 2021-06-08 Massimo Bertolini, Marco Adamo Seveso, Rodolfo Venerucci
This article proves a case of the p-adic Birch and Swinnerton–Dyer conjecture for Garrett p-adic L-functions of (Bertolini et al. in On p-adic analogues of the Birch and Swinnerton–Dyer conjecture for Garrett L-functions, 2021), in the imaginary dihedral exceptional zero setting of extended analytic rank 4.
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New Computational Formulas for Special Numbers and Polynomials Derived from Applying Trigonometric Functions to Generating Functions Milan J. Math. (IF 1.7) Pub Date : 2021-05-12 Neslihan Kilar, Yilmaz Simsek
The aim of this paper is to apply trigonometric functions with functional equations of generating functions. Using the resulted new equations and formulas from this application, we obtain many special numbers and polynomials such as the Stirling numbers, Bernoulli and Euler type numbers, the array polynomials, the Catalan numbers, and the central factorial numbers. We then introduce combinatorial sums
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Singularities of Solutions of Hamilton–Jacobi Equations Milan J. Math. (IF 1.7) Pub Date : 2021-05-07 Piermarco Cannarsa, Wei Cheng
This is a survey paper on the quantitative analysis of the propagation of singularities for the viscosity solutions to Hamilton–Jacobi equations in the past decades. We also review further applications of the theory to various fields such as Riemannian geometry, Hamiltonian dynamical systems and partial differential equations.