Related papers: Symmetry in Serrin-type overdetermined problems
In this paper we study a semilinear elliptic problem on a bounded domain in $\R^2$ with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymtotic estimates…
We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…
This paper deals with symmetry phenomena for solutions of the Dirichlet problem involving semilinear PDEs on Riemannian domains. We shall present a rather general framework where the symmetry problem can be formulated and provide some…
This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as $\e\to 0$, and the domain is…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
In this note we construct smooth bounded domains $\Omega \subset \mathbb R^2$, other than disks, for which the overdetermined problem $$ \left\{ \begin{alignedat}{2} \Delta u + \lambda u &= 0 &\qquad& \text{ in } \Omega, \newline u &= b…
In this paper we construct nontrivial exterior domains $\Omega \subset \mathbb{R}^N$, for all $N\geq 2$, such that the problem $$\left\{ {ll} -\Delta u +u -u^p=0,\ u >0 & \mbox{in }\; \Omega, {1mm] \ u= 0 & \mbox{on }\; \partial \Omega,…
In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap…
In the present paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations which are locally stable.
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of…
In this paper we approach the problem of perturbation from symmetry of strongly indefinite elliptic systems in dimension N>=3. We prove the existence of infinitely many solutions under suitable growth coinditions on the nonlinear terms.
We establish the existence of positive solutions to a general class of overdetermined semilinear elliptic boundary problems on suitable bounded open sets $\Omega\subset\mathbb{R}^n$. Specifically, for $n\leq 4$ and under mild technical…
An accurate approximation of solutions to elliptic problems in infinite domains is challenging from a computational point of view. This is due to the need to replace the infinite domain with a sufficiently large and bounded computational…
The goal of this paper is to study some possibly degenerate elliptic equation in a bounded domain with a nonlinear boundary condition involving measure data. We investigate two types of problems: the first one deals with the laplacian in a…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
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…
We study periodic homogenization problems for second-order pde in half-space type domains with Neumann boundary conditions. In particular, we are interested in "singular problems" for which it is necessary to determine both the homogenized…
We consider the solution of the problem $$ -\Delta u=f(u) \ \mbox{ and } \ u>0 \ \ \mbox{ in } \ \Omega, \ \ u=0 \ \mbox{ on } \ \Gamma, $$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with boundary $\Gamma$ of class $C^{2,\tau}$,…
We prove the existence of nontrivial unbounded domains $\O$ in the Euclidean space $\R^d$ for which the Dirichlet eigenvalue problem for the Laplacian on $\Omega$ admits sign-changing eigenfunctions with constant Neumann values on $\partial…