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arXiv · 1509.04001

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

Serena Dipierro·Nicola Soave·Enrico Valdinoci
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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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Serena Dipierro, Nicola Soave, Enrico Valdinoci. 2015-09-14. On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data. https://arxiv.org/abs/1509.04001

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