(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dipierro, Serena; Soave, Nicola; Valdinoci, Enrico
We study reaction-diffusion equations in cylinders with possibly
nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We
provide a geometric Poincare-type inequality and classification results for
stable solutions, and we apply them to the study of an associated nonlocal
problem. We also establish a counterexample in the corresponding framework
for the fractional Laplacian.
