样式: 排序: IF: - GO 导出 标记为已读
-
Asymptotic behaviour of solutions to the anisotropic doubly critical equation Calc. Var. (IF 2.1) Pub Date : 2024-03-15 Francesco Esposito, Luigi Montoro, Berardino Sciunzi, Domenico Vuono
The aim of this paper is to deal with the anisotropic doubly critical equation $$\begin{aligned} -\Delta _p^H u - \frac{\gamma }{[H^\circ (x)]^p} u^{p-1} = u^{p^*-1} \qquad \text {in } {\mathbb {R}}^N, \end{aligned}$$ where H is in some cases called Finsler norm, \(H^\circ \) is the dual norm, \(1
-
Magneto-micropolar boundary layers theory in Sobolev spaces without monotonicity: well-posedness and convergence theory Calc. Var. (IF 2.1) Pub Date : 2024-03-14 Xue-yun Lin, Cheng-jie Liu, Ting Zhang
In this paper, we study the well-posedness theory of the magneto-micropolar boundary layer and justify the high Reynolds numbers limit for the magneto-micropolar system with Prandtl boundary layer expansion. If the initial tangential magnetic field is nondegenerate, we obtain the local-in-time existence, uniqueness of solutions for the incompressible magneto-micropolar boundary layer equations with
-
On the hydrostatic Navier–Stokes equations with Gevrey class 2 data Calc. Var. (IF 2.1) Pub Date : 2024-03-14
Abstract In this paper, we study the two-dimensional hydrostatic Navier–Stokes equations in the strip domain \({\mathbb R}\times \mathbb {T}\) . Motivated by Gérard-Varet et al. (Anal PDE 13(5):1417–1455 2020), we obtain the local well-posedness result in Gevrey class 2 when the initial data is a small perturbation of some convex function. Then we justify strictly the limit from the anisotropic Navier–Stokes
-
Local well-posedness for incompressible neo-Hookean elastic equations in almost critical Sobolev spaces Calc. Var. (IF 2.1) Pub Date : 2024-03-07 Huali Zhang
Inspired by a pioneer work of Andersson and Kapitanski (Arch Ration Mech Anal 247(2):Paper No. 21, 76 pp, 2023), we prove the local well-posedness of the Cauchy problem of incompressible neo-Hookean equations if the initial deformation and velocity belong to \(H^{\frac{n+2}{2}+}({\mathbb {R}}^n) \times H^{\frac{n}{2}+}({\mathbb {R}}^n)\) (\(n=2,3\)), where \(\frac{n+2}{2}\) and \(\frac{n}{2}\) is respectively
-
Stability of quermassintegral inequalities along inverse curvature flows Calc. Var. (IF 2.1) Pub Date : 2024-03-07 Caroline VanBlargan, Yi Wang
In this paper, we consider the stability of quermassintegral inequalities along a inverse curvature flow. We choose a special rescaling of the flow such that the k-th quermassintegral is decreasing and the \(k-1\)-th quermassintegral is preserved. Along this rescaled flow, we prove that the decreasing rate of the k-th quermassintegral is faster than the Fraenkel asymmetry of the domain along the flow
-
The Dirichlet problem for Lévy-stable operators with $$L^2$$ -data Calc. Var. (IF 2.1) Pub Date : 2024-03-07 Florian Grube, Thorben Hensiek, Waldemar Schefer
-
On the weak Harnack estimate for nonlocal equations Calc. Var. (IF 2.1) Pub Date : 2024-03-07
Abstract We prove a weak Harnack estimate for a class of doubly nonlinear nonlocal equations modelled on the nonlocal Trudinger equation $$\begin{aligned} \partial _t(|u|^{p-2}u) + (-\Delta _p)^s u = 0 \end{aligned}$$ for \(p\in (1,\infty )\) and \(s \in (0,1)\) . Our proof relies on expansion of positivity arguments developed by DiBenedetto, Gianazza and Vespri adapted to the nonlocal setup. Even
-
A homogenization result in finite plasticity Calc. Var. (IF 2.1) Pub Date : 2024-03-07
Abstract We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we establish the \(\Gamma \) -convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to \(\textsf{SL}(3)\)
-
Asymptotic stability of boundary layer to the multi-dimensional isentropic Euler-Poisson equations arising in plasma physics Calc. Var. (IF 2.1) Pub Date : 2024-03-07 Yufeng Chen, Wenjuan Ding, Junpei Gao, Mengyuan Lin, Lizhi Ruan
-
Towards existence theorems to affine p-Laplace equations via variational approach Calc. Var. (IF 2.1) Pub Date : 2024-03-07 Edir Júnior Ferreira Leite, Marcos Montenegro
The present work deals with theory of critical points to the energy functional on \(W^{1,p}_0(\Omega )\) defined by $$\begin{aligned} \Phi _\mathcal{A}(u) = \frac{1}{p} \mathcal{E}^p_{p,\Omega }(u) - \int _\Omega F(x,u)\,dx, \end{aligned}$$ where \(\mathcal{E}^p_{p,\Omega }\) stands for the affine p-energy introduced for \(p > 1\) by Lutwak et al. (J Differ Geom 62:17–38, 2002). Its development is
-
Multiplicity one for min–max theory in compact manifolds with boundary and its applications Calc. Var. (IF 2.1) Pub Date : 2024-03-07 Ao Sun, Zhichao Wang, Xin Zhou
We prove the multiplicity one theorem for min–max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approach this, we develop existence and regularity theory for free boundary hypersurface with prescribed mean curvature, which includes the regularity theory for minimizers, compactness theory, and a generic min–max theory with
-
On the construction of non-simple blow-up solutions for the singular Liouville equation with a potential Calc. Var. (IF 2.1) Pub Date : 2024-03-07
Abstract We are concerned with the existence of blowing-up solutions to the following boundary value problem $$\begin{aligned} -\Delta u= \lambda V(x) e^u-4\pi N {\varvec{\delta }}_0 \;\hbox { in } B_1,\quad u=0 \;\hbox { on }\partial B_1, \end{aligned}$$ where \(B_1\) is the unit ball in \(\mathbb {R}^2\) centered at the origin, V(x) is a positive smooth potential, N is a positive integer ( \(N\ge
-
Normalized ground states for the fractional Schrödinger–Poisson system with critical nonlinearities Calc. Var. (IF 2.1) Pub Date : 2024-03-02 Yuxi Meng, Xiaoming He
In this paper we study the existence and properties of ground states for the fractional Schrödinger–Poisson system with combined power nonlinearities $$\begin{aligned}{\left\{ \begin{array}{ll}\displaystyle (-\Delta )^su-\phi |u|^{2^*_s-3}u=\lambda u+\mu |u|^{q-2}u+|u|^{2^*_s-2}u, &{}x \in {\mathbb {R}}^{3},\\ (-\Delta )^{s}\phi =|u|^{2^*_s-1}, &{}x \in {\mathbb {R}}^{3},\end{array}\right. } \end{aligned}$$
-
Singular solutions to the $$\sigma _k$$ -Yamabe equation with prescribed asymptotics Calc. Var. (IF 2.1) Pub Date : 2024-02-27 Zirui Li, Qing Han
In this work, we explore the asymptotic behaviors of positive solutions to the \(\sigma _k\)-Yamabe equation. Extending Han and Li’s previous work on the Yamabe equation, we demonstrate that for every approximate solution \({\widetilde{w}}\) of a specified order, there exists a corresponding solution w that closely approximates \({\widetilde{w}}\). Our study further presents a concrete method for constructing
-
Matrix Li–Yau–Hamilton estimates under Ricci flow and parabolic frequency Calc. Var. (IF 2.1) Pub Date : 2024-02-26 Xiaolong Li, Qi S. Zhang
We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow. We then apply these estimates to establish the monotonicity of parabolic frequencies up to correction factors. As applications, we obtain some unique continuation results under the nonnegativity of sectional or complex sectional curvature
-
The Lavrentiev phenomenon in calculus of variations with differential forms Calc. Var. (IF 2.1) Pub Date : 2024-02-22 Anna Kh. Balci, Mikhail Surnachev
In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to several models, including the double phase, borderline case of double phase potential, and variable exponent. The results for the borderline case of double phase potential
-
Transportation onto log-Lipschitz perturbations Calc. Var. (IF 2.1) Pub Date : 2024-02-20 Max Fathi, Dan Mikulincer, Yair Shenfeld
We establish sufficient conditions for the existence of globally Lipschitz transport maps between probability measures and their log-Lipschitz perturbations, with dimension-free bounds. Our results include Gaussian measures on Euclidean spaces and uniform measures on spheres as source measures. More generally, we prove results for source measures on manifolds satisfying strong curvature assumptions
-
Global regularity for nonlinear systems with symmetric gradients Calc. Var. (IF 2.1) Pub Date : 2024-02-16 Linus Behn, Lars Diening
We study global regularity of nonlinear systems of partial differential equations depending on the symmetric part of the gradient with Dirichlet boundary conditions. These systems arise from variational problems in plasticity with power growth. We cover the full range of exponents \(p \in (1,\infty )\). As a novelty the degenerate case for \(p>2\) is included. We present a unified approach for all
-
The weak solutions to complex Hessian equations Calc. Var. (IF 2.1) Pub Date : 2024-02-12 Wei Sun
In this paper, we shall study existence of weak solutions to complex Hessian equations on compact Hermitian manifolds. With appropriate assumptions, it is possible to obtain weak solutions in different senses.
-
Dirichlet problem for Krylov type equation in conformal geometry Calc. Var. (IF 2.1) Pub Date : 2024-02-12
Abstract In this paper, we study a class of nonlinear elliptic equations in the Krylov type, which can be viewed as a generalization of the Hessian equation for Schouten tensor. After a conformal change, we considered the Dirichlet problem for a modified Schouten tensor in the smooth closed Riemannian manifold with smooth boundary. A unique k-admissible solution can be assured under some suitable settings
-
Least gradient problem with Dirichlet condition imposed on a part of the boundary Calc. Var. (IF 2.1) Pub Date : 2024-02-12 Wojciech Górny
-
Inertial evolution of non-linear viscoelastic solids in the face of (self-)collision Calc. Var. (IF 2.1) Pub Date : 2024-02-10 Antonín Češík, Giovanni Gravina, Malte Kampschulte
We study the time evolution of non-linear viscoelastic solids in the presence of inertia and (self-)contact. For this problem we prove the existence of weak solutions for arbitrary times and initial data, thereby solving an open problem in the field. Our construction directly includes the physically correct, measure-valued contact forces and thus obeys conservation of momentum and an energy balance
-
The $$L^p$$ -Fisher–Rao metric and Amari–C̆encov $$\alpha $$ -Connections Calc. Var. (IF 2.1) Pub Date : 2024-02-10 Martin Bauer, Alice Le Brigant, Yuxiu Lu, Cy Maor
-
Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic maps Calc. Var. (IF 2.1) Pub Date : 2024-02-10 Hugo Lavenant, Léonard Monsaingeon, Luca Tamanini, Dmitry Vorotnikov
If \(u: \Omega \subset \mathbb {R}^d \rightarrow \textrm{X}\) is a harmonic map valued in a metric space \(\textrm{X}\) and \(\textsf{E}: \textrm{X}\rightarrow \mathbb {R}\) is a convex function, in the sense that it generates an \(\textrm{EVI}_0\)-gradient flow, we prove that the pullback \(\textsf{E}\circ u: \Omega \rightarrow \mathbb {R}\) is subharmonic. This property was known in the smooth Riemannian
-
Einstein manifolds and curvature operator of the second kind Calc. Var. (IF 2.1) Pub Date : 2024-02-09 Zhi-Lin Dai, Hai-Ping Fu
We prove that a compact Einstein manifold of dimension \(n\ge 4\) with nonnegative curvature operator of the second kind is a constant curvature space by Bochner technique. Moreover, we obtain that compact Einstein manifolds of dimension \(n\ge 11\) with \(\left[ \frac{n+2}{4} \right] \)-nonnegative curvature operator of the second kind, \(4\ (\text{ resp. },8,9,10)\)-dimensional compact Einstein manifolds
-
Bernstein type theorems of translating solitons of the mean curvature flow in higher codimension Calc. Var. (IF 2.1) Pub Date : 2024-02-07 Hongbing Qiu
By carrying out point-wise estimates for the mean curvature, we prove Bernstein type theorems of complete translating solitons of the mean curvature flow in higher codimension under various geometric conditions.
-
An existence result for the Kazdan–Warner equation with a sign-changing prescribed function Calc. Var. (IF 2.1) Pub Date : 2024-02-07 Linlin Sun, Jingyong Zhu
-
The well-posedness of incompressible rotational jet flows with gravity Calc. Var. (IF 2.1) Pub Date : 2024-02-01 Jianfeng Cheng, Zhenlei Pei
-
A chemotaxis system with singular sensitivity for burglaries in the higher-dimensional settings: generalized solvability and long-time behavior Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Bin Li, Li Xie
We study the no-flux initial-boundary value problem of a chemotaxis system with singular sensitivity of the following form $$\begin{aligned} \left\{ \begin{aligned}&u_t= \Delta u-\chi \nabla \cdot \left( u\nabla \ln v\right) - u+ g_1, \\&v_t=\Delta v- v+ uv(1-v)+g_2, \end{aligned} \right. \end{aligned}$$(⋆) over a bounded domain \(\Omega \subset {\mathbb {R}}^n\), with chemotaxis coefficient \(\chi
-
Degenerate stability of the Caffarelli–Kohn–Nirenberg inequality along the Felli–Schneider curve Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Rupert L. Frank, Jonas W. Peteranderl
We show that the Caffarelli–Kohn–Nirenberg (CKN) inequality holds with a remainder term that is quartic in the distance to the set of optimizers for the full parameter range of the Felli–Schneider (FS) curve. The fourth power is best possible. This is due to the presence of non-trivial zero modes of the Hessian of the deficit functional along the FS-curve. Following an iterated Bianchi–Egnell strategy
-
On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Jakub Maksymiuk
In this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function \(c(x,A)=|A[x]^2|\). We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular
-
Linear and nonlinear analysis of the viscous Rayleigh–Taylor system with Navier-slip boundary conditions Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Tiến-Tài Nguyễn
In this paper, we are interested in the linear and the nonlinear Rayleigh–Taylor instability for the gravity-driven incompressible Navier–Stokes equations with Navier-slip boundary conditions around a smooth increasing density profile \(\rho _0(x_2)\) in a slab domain \(2\pi L\mathbb T\times (-1,1)\) (\(L>0\), \(\mathbb T\) is the usual 1D torus). The linear instability study of the viscous Rayleigh–Taylor
-
Local well-posedness of the 1d compressible Navier–Stokes system with rough data Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
This paper presents a new approach to the local well-posedness of the 1d compressible Navier–Stokes systems with rough initial data. Our approach is based on establishing some smoothing and Lipschitz-type estimates for the 1d parabolic equation with piecewise continuous coefficients.
-
Deformation of discrete conformal structures on surfaces Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Xu Xu
In Glickenstein (J Differ Geom 87: 201–237, 2011), Glickenstein introduced the discrete conformal structures on polyhedral surfaces in an axiomatic approach from Riemannian geometry perspective. It includes Thurston’s circle packings, Bowers–Stephenson’s inversive distance circle packings and Luo’s vertex scalings as special cases. In this paper, we study the deformation of Glickenstein’s discrete
-
Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Blair Davey, Mariana Smit Vega Garcia
This paper continues the study initiated in Davey (Arch Ration Mech Anal 228:159–196, 2018), where a high-dimensional limiting technique was developed and used to prove certain parabolic theorems from their elliptic counterparts. In this article, we extend these ideas to the variable-coefficient setting. This generalized technique is demonstrated through new proofs of three important theorems for
-
A rigorous justification of the Mittleman’s approach to the Dirac–Fock model Calc. Var. (IF 2.1) Pub Date : 2024-01-28
Abstract In this paper, we study the relationship between the Dirac–Fock model and the electron-positron Hartree–Fock model. We justify the Dirac–Fock model as a variational approximation of QED when the vacuum polarization is neglected and when the fine structure constant \(\alpha \) is small and the velocity of light c is large. As a byproduct, we also prove, when \(\alpha \) is small or c is large
-
Isoperimetric inequalities and regularity of A-harmonic functions on surfaces Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Tomasz Adamowicz, Giona Veronelli
-
Cahn–Hillard and Keller–Segel systems as high-friction limits of Euler–Korteweg and Euler–Poisson equations Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Dennis Gallenmüller, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Jakub Woźnicki
We consider a combined system of Euler–Korteweg and Euler–Poisson equations with friction and exponential pressure with exponent \(\gamma > 1\). We show the existence of dissipative measure-valued solutions in the cases of repulsive and attractive potential in Euler–Poisson system. The latter case requires additional restriction on \(\gamma \). Furthermore in case of \(\gamma \ge 2\) we show that the
-
Large time behavior of the solutions to 3D incompressible MHD system with horizontal dissipation or horizontal magnetic diffusion Calc. Var. (IF 2.1) Pub Date : 2024-01-28 Yang Li
In this paper, we consider the asymptotic behavior of global solutions to 3D anisotropic incompressible MHD systems. For the 3D MHD system with horizontal dissipation and full magnetic diffusion, it is shown that \(u_{\textrm{h}}(t)\) decays at the rate of \(O\left( t^{-(1-\frac{1}{p})}\right) \), \(u_3(t)\) decays at the rate of \(O\left( t^{-\frac{3}{2}(1-\frac{1}{p})}\right) \) and B(t) decays at
-
Block-radial symmetry breaking for ground states of biharmonic NLS Calc. Var. (IF 2.1) Pub Date : 2024-01-28
Abstract We prove that the biharmonic NLS equation $$\begin{aligned} \Delta ^2 u +2\Delta u+(1+\varepsilon )u=|u|^{p-2}u\,\,\, in {\mathbb {R}}^d \end{aligned}$$ has at least \(k+1\) geometrically distinct solutions if \(\varepsilon >0\) is small enough and \(2
-
An alternative proof for small energy implies regularity for radially symmetric $$(1+2)$$ -dimensional wave maps Calc. Var. (IF 2.1) Pub Date : 2024-01-23 Ning-An Lai, Yi Zhou
In this paper we are interested in showing an alternative and simple proof for small energy implies regularity to the Cauchy problem of radially symmetric wave maps from the \((1+2)\)-dimensional Minkowski space to an arbitrary smooth Riemannian manifold \(\mathcal {M}\subset \textbf{R}^n\) with bounded first derivatives of the second fundamental form. Then, combining the classical works of Struwe
-
Regularity of the $$p-$$ Bergman kernel Calc. Var. (IF 2.1) Pub Date : 2024-01-22 Bo-Yong Chen, Yuanpu Xiong
We show that the \(p-\)Bergman kernel \(K_p(z)\) on a bounded domain \(\Omega \) is of locally \(C^{1,1}\) for \(p\ge 1\).The proof is based on the locally Lipschitz continuity of the off-diagonal \(p-\)Bergman kernel \(K_p(\zeta ,z)\) for fixed \(\zeta \in \Omega \). Global irregularity of \(K_p(\zeta ,z)\) is presented for some smooth strongly pseudoconvex domains when \(p\gg 1\). As an application
-
Absence and presence of Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents Calc. Var. (IF 2.1) Pub Date : 2024-01-18
Abstract We study classes of weights ensuring the absence and presence of the Lavrentiev’s phenomenon for double phase functionals upon every choice of exponents. We introduce a new sharp scale for weights for which there is no Lavrentiev’s phenomenon up to a counterexample we provide. This scale embraces the sharp range for \(\alpha \) -Hölder continuous weights. Moreover, it allows excluding the
-
Vortex sheet solutions for the Ginzburg–Landau system in cylinders: symmetry and global minimality Calc. Var. (IF 2.1) Pub Date : 2024-01-17 Radu Ignat, Mircea Rus
We consider the Ginzburg–Landau energy \(E_{\varepsilon }\) for \(\mathbb {R}^M\)-valued maps defined in a cylinder shape domain \(B^N\times (0,1)^n\) satisfying a degree-one vortex boundary condition on \(\partial B^N\times (0,1)^n\) in dimensions \(M\ge N\ge 2\) and \(n\ge 1\). The aim is to study the radial symmetry of global minimizers of this variational problem. We prove the following: if \(N\ge
-
Existence of blowup solutions to the semilinear heat equation with double power nonlinearity Calc. Var. (IF 2.1) Pub Date : 2024-01-09 Junichi Harada
We are concerned with the semilinear heat equation \(u_t=\Delta u+|u|^{p-1}u-|u|^{q-1}u\) in \({\mathbb {R}}^n\times (0,T)\), where \(n=5\), \(p=\frac{n+2}{n-2}\), and \(q\in (0,1)\). A goal of this paper is to show the existence of a new type of blowup solutions for this equation. This blowup solution is obtained by connecting a specific blowup solution of \(u_t=\Delta u+|u|^{p-1}u\) and a specific
-
An obstacle problem arising from American options pricing: regularity of solutions Calc. Var. (IF 2.1) Pub Date : 2024-01-12 Henrique Borrin, Diego Marcon
-
New homogenization results for convex integral functionals and their Euler–Lagrange equations Calc. Var. (IF 2.1) Pub Date : 2024-01-12 Matthias Ruf, Mathias Schäffner
We study stochastic homogenization for convex integral functionals $$\begin{aligned} u\mapsto \int _D W(\omega ,\tfrac{x}{\varepsilon },\nabla u)\,\textrm{d}x,\quad \text{ where }\quad u:D\subset {\mathbb {R}}^d\rightarrow {\mathbb {R}}^m, \end{aligned}$$ defined on Sobolev spaces. Assuming only stochastic integrability of the map \(\omega \mapsto W(\omega ,0,\xi )\), we prove homogenization results
-
Bourgain-Brezis-Mironescu formula for $$W^{s,p}_q$$ -spaces in arbitrary domains Calc. Var. (IF 2.1) Pub Date : 2024-01-09 Kaushik Mohanta
Under certain restrictions on s, p, q, the Triebel-Lizorkin spaces can be viewed as generalised fractional Sobolev spaces \(W^{s,p}_q\). In this article, we show that the Bourgain-Brezis-Mironescu formula holds for \(W^{s,p}_q\)-seminorms in arbitrary domain. This addresses an open question raised by Brazke-Schikorra-Yung (Calc Var Partial Differ Equ 62(2):41–33, (2023).
-
Interactions in the Lorentz force equation Calc. Var. (IF 2.1) Pub Date : 2024-01-08 Cristian Bereanu
In this paper we consider for arbitrary \(\mu \in \mathbb {R}\) the Lorentz force equation $$\begin{aligned} \left( \frac{q'}{\sqrt{1-|q'|^2}}\right) ' + \mu q= -\nabla _q V-\frac{\partial W}{\partial t}+q'\times \text {curl}_q\, W, \end{aligned}$$ with a Kepler type electric potential \(V+\frac{\mu }{2}|q|^2\) and a smooth magnetic potential W which are T-periodic in time. We show that two fundamentally
-
Jumps in Besov spaces and fine properties of Besov and fractional Sobolev functions Calc. Var. (IF 2.1) Pub Date : 2024-01-06 Paz Hashash, Arkady Poliakovsky
In this paper we analyse functions in Besov spaces \(B^{1/q}_{q,\infty }(\mathbb {R}^N,\mathbb {R}^d),q\in (1,\infty )\), and functions in fractional Sobolev spaces \(W^{r,q}(\mathbb {R}^N,\mathbb {R}^d),r\in (0,1),q\in [1,\infty )\). We prove for Besov functions \(u\in B^{1/q}_{q,\infty }(\mathbb {R}^N,\mathbb {R}^d)\) the summability of the difference between one-sided approximate limits in power
-
Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities Calc. Var. (IF 2.1) Pub Date : 2024-01-06 Sun-Sig Byun, Deepak Kumar, Ho-Sik Lee
A non-homogeneous mixed local and nonlocal problem in divergence form is investigated for the validity of the global Calderón–Zygmund estimate for the weak solution to the Dirichlet problem of a nonlinear elliptic equation. We establish an optimal Calderón–Zygmund theory by finding not only a minimal regularity requirement on the mixed local and nonlocal operators but also a lower level of geometric
-
Lipschitz regularity for solutions of a general class of elliptic equations Calc. Var. (IF 2.1) Pub Date : 2023-12-22 Greta Marino, Sunra Mosconi
We prove local Lipschitz regularity for local minimisers of $$\begin{aligned} W^{1,1}(\Omega )\ni v\mapsto \int _\Omega F(Dv)\, dx \end{aligned}$$ where \(\Omega \subseteq {\mathbb {R}}^N\), \(N\ge 2\) and \(F:{\mathbb {R}}^N\rightarrow {\mathbb {R}}\) is a quasiuniformly convex integrand in the sense of Kovalev and Maldonado (Ill J Math 49:1039–1060, 2005), i. e. a convex \(C^1\)-function such that
-
Global weak solutions in nonlinear 3D thermoelasticity Calc. Var. (IF 2.1) Pub Date : 2023-12-22 Tomasz Cieślak, Boris Muha, Srđan Trifunović
Here we study a nonlinear thermoelasticity hyperbolic-parabolic system describing the balance of momentum and internal energy of a heat-conducting elastic body, preserving the positivity of temperature. So far, no global existence results in such a natural case were available. Our result is obtained by using thermodynamically justified variables which allow us to obtain an equivalent system in which
-
Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth Calc. Var. (IF 2.1) Pub Date : 2023-12-22 Stefano Almi, Dario Reggiani, Francesco Solombrino
A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided. Our analysis is based on a non-trivial adaptation of the blow-up (Ambrosio in Nonlinear Anal 23:405–425, 1994) and of the global method for relaxation (Bouchitté in Arch Ration Mech Anal 165:187–242, 2002) to the setting of generalized special function
-
Quantitative symmetry in a mixed Serrin-type problem for a constrained torsional rigidity Calc. Var. (IF 2.1) Pub Date : 2023-12-22 Rolando Magnanini, Giorgio Poggesi
-
Hölder regularity for parabolic fractional p-Laplacian Calc. Var. (IF 2.1) Pub Date : 2023-12-19 Naian Liao
Local Hölder regularity is established for certain weak solutions to a class of parabolic fractional p-Laplace equations with merely measurable kernels. The proof uses DeGiorgi’s iteration and refines DiBenedetto’s intrinsic scaling method. The control of a nonlocal integral of solutions in the reduction of oscillation plays a crucial role and entails delicate analysis in this intrinsic scaling scenario
-
Bubbling phenomenon for semilinear Neumann elliptic equations of critical exponential growth Calc. Var. (IF 2.1) Pub Date : 2023-12-19 Lu Chen, Guozhen Lu, Caifeng Zhang
In the past few decades, much attention has been paid to the bubbling problem for semilinear Neumann elliptic equations with the critical and subcritical polynomial nonlinearity, much less is known if the polynomial nonlinearity is replaced by the exponential nonlinearity. In this paper, we consider the following semilinear Neumann elliptic problem with the Trudinger–Moser exponential growth: $$\begin{aligned}
-
Anchored heat kernel upper bounds on graphs with unbounded geometry and anti-trees Calc. Var. (IF 2.1) Pub Date : 2023-12-19 Matthias Keller, Christian Rose
-
A continuous dependence estimate for viscous Hamilton–Jacobi equations on networks with applications Calc. Var. (IF 2.1) Pub Date : 2023-12-11 Fabio Camilli, Claudio Marchi
We study continuous dependence estimates for viscous Hamilton–Jacobi equations defined on a network \(\Gamma \). Given two Hamilton–Jacobi equations, we prove an estimate of the \(C^2\)-norm of the difference between the corresponding solutions in terms of the distance among the Hamiltonians. We also provide two applications of the previous estimate: the first one is an existence and uniqueness result
-
A sharp convergence theorem for the mean curvature flow in the sphere Calc. Var. (IF 2.1) Pub Date : 2023-12-11 Dong Pu
In this paper, we prove a sharp convergence theorem for the mean curvature flow of arbitrary codimension in the sphere \( {\mathbb {S}}^{n+p}(\frac{1}{\sqrt{{\bar{K}}}})\). Note that Baker proved a convergence theorem for the mean curvature flow in the sphere under the pinching condition \(|A|^2\le \frac{1}{n-1}|H|^2+2{\bar{K}} \), where A is the second fundamental form and H is the mean curvature