17 citations · 32 across the 7 of their papers we have counts for
9 papers
Optimal regularity of stable solutions to nonlinear equations involving the -Laplacian
Xavier Cabre, Pietro Miraglio, Manel Sanchon
We consider the equation in a smooth bounded domain of , where is the -Laplace operator. Explicit examples of unbounded stable energy solution…
Antisymmetry of solutions for some weighted elliptic problems
Xavier Cabre, Marcello Lucia, Manel Sanchon +1
This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-…
A priori estimates for semistable solutions of semilinear elliptic equations
Xavier Cabre, Manel Sanchon, Joel Spruck
We consider positive semistable solutions of with zero Dirichlet boundary condition, where is a uniformly elliptic operator and is a positive, nondec…
Regularity of stable solutions to semilinear elliptic equations on Riemannian models
Daniele Castorina, Manel Sanchon
We consider the reaction-diffusion problem in with zero Dirichlet boundary condition, posed in a geodesic ball with radius of a…
estimates for the extremal solution of reaction-diffusion problems
Manel Sanchon
We establish a new estimate for the extremal solution of in a smooth bounded domain of , which is convex, for arbitrary posit…
Regularity of stable solutions of -Laplace equations through geometric Sobolev type inequalities
Daniele Castorina, Manel Sanchon
In this paper we prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears i…