15-98 Serena Dipierro, Nicola Soave, Enrico Valdinoci

On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data (99K, LaTeX) Sep 7, 15

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Abstract. We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-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.

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