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Our work proposes a unified approach to three different topics in a general Riemannian setting: splitting theorems, symmetry results and overdetermined elliptic problems. By the existence of a stable solution to the semilinear equation…

Analysis of PDEs · Mathematics 2012-10-23 Alberto Farina , Luciano Mari , Enrico Valdinoci

We investigate existence and nonexistence of stationary stable nonconstant solutions, i.e. patterns, of semilinear parabolic problems in bounded domains of Riemannian manifolds satisfying Robin boundary conditions. These problems arise in…

Analysis of PDEs · Mathematics 2015-07-27 Catherine Bandle , Paolo Mastrolia , Dario D. Monticelli , Fabio Punzo

We present existence and nonexistence results on the solution of an overdetermined problem for the normalized p-Laplacian in a bounded open set, with p ranging from 1 to infinity. More precisely we consider a non-constant Neumann condition…

Analysis of PDEs · Mathematics 2024-03-06 Lucio Cadeddu , Antonio Greco , Benyam Mebrate

We establish the existence of weak solutions of a nonlinear radiation-type boundary value problem for elliptic equation on divergence form with discontinuous leading coefficient. Quantitative estimates play a crucial role on the real…

Analysis of PDEs · Mathematics 2015-07-23 Luisa Consiglieri

Nonlinear elliptic Neumann problems, possibly in irregular domains and with data affected by low integrability properties, are taken into account. Existence, uniqueness and continuous dependence on the data of generalized solutions are…

Analysis of PDEs · Mathematics 2015-05-13 A. Alvino , A. Cianchi , V. Maz'ya , A. Mercaldo

In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain…

Analysis of PDEs · Mathematics 2024-06-28 Xiaoli Yu , Xingyong Zhang

In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian.

Analysis of PDEs · Mathematics 2019-03-27 J. Carmona , E. Colorado , T. Leonori , A. Ortega

We consider the Dirichlet problem for quasilinear elliptic equations with Musielak-Orlicz (p,q)-growth and non-logarithmic conditions on the coefficients. A sufficient Wiener-type condition for the regularity of a boundary point is…

Analysis of PDEs · Mathematics 2021-09-20 Oleksandr V. Hadzhy , Mykhailo V. Voitovych

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…

Classical Analysis and ODEs · Mathematics 2015-05-20 Pascal Auscher , Andreas Rosén

We study nonlinear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that the ergodic constant appears in the (possibly nonlinear) Neumann boundary conditions. We provide, for bounded…

Analysis of PDEs · Mathematics 2015-06-26 Guy Barles , Francesca Da Lio

We consider the semilinear elliptic equation $-\Delta u =\lambda f(u)$ in a smooth bounded domain $\Omega$ of $R^{n}$ with Dirichielt boundary condition, where $f$ is a $C^{1}$ positive and nondeccreasing function in $[0,\infty)$ such that…

Analysis of PDEs · Mathematics 2015-08-27 Asadollah Aghajani

In this note we derive large-scale regularity properties of solutions to second-order linear elliptic equations with random coefficients on the half- space with homogeneous Neumann boundary data; it is a companion to arXiv:1604.02717 in…

Analysis of PDEs · Mathematics 2017-03-14 Claudia Raithel

For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary…

Analysis of PDEs · Mathematics 2020-04-22 Jussi Behrndt , Jonathan Rohleder

We find a solution of a quasilinear elliptic equation with Dirichlet's boundary condition on a smooth bounded domain and involving an unbounded continuous nonlinearity with oscillatory behavior near the origin.

Analysis of PDEs · Mathematics 2017-03-02 Rafael dos Reis Abreu , Anderson Luis Albuquerque de Araujo

In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…

Analysis of PDEs · Mathematics 2016-11-22 Tujin Kim , Daomin Cao

This article studies the Dirichlet problem for a class of degenerate fully nonlinear elliptic equations on Riemannian manifolds with \textit{mean concave} boundary in the sense that the mean curvature of the boundary is…

Analysis of PDEs · Mathematics 2020-06-16 Rirong Yuan

In this paper, we prove the existence of a family of non trivial compact subdomains $\O$ in the manifold $\mathcal{M}=\R^N\times \R/2\pi\Z, N\geq 2$ for which the overdetermined Neumann boundary value problem \begin{align}\label{Neumann1}…

Analysis of PDEs · Mathematics 2025-05-14 Ignace Aristide Minlend , Jing Wu

In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Francois Ebobisse , Marcello Ponsiglione

In this paper, we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary. If the domain…

Analysis of PDEs · Mathematics 2021-05-14 Jingqi Liang , Lihe Wang , Chunqin Zhou

In this paper we prove the boundedness and H\"older continuity of quasilinear elliptic problems involving variable exponents for a homogeneous Dirichlet and a nonhomogeneous Neumann boundary condition, respectively. The novelty of our work…

Analysis of PDEs · Mathematics 2022-01-10 Ky Ho , Yun-Ho Kim , Patrick Winkert , Chao Zhang