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

2015/09/14 by Serena Dipierro, Nicola Soave, Dipierro, Serena +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1509.04001

openalex publication_date 2015/09/14 · arxiv created 2016/06/25 · arxiv updated 2016/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincaré-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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