On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data

摘要

We study reaction-diffusion equations in cylinders with possibly nonlineardiffusion and possibly nonlinear Neumann boundary conditions. We provide ageometric Poincar\'e-type inequality and classification results for stablesolutions, and we apply them to the study of an associated nonlocal problem. Wealso establish a counterexample in the corresponding framework for thefractional Laplacian.