WIAS Preprint No. 2152, (2015)

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



Authors

  • Dipierro, Serena
  • Soave, Nicola
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35J62 35J92 35J93 35B53

Keywords

  • Stability, symmetry results, classification of solution, reaction-diffusion equations, nonlocal equations

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.

Appeared in

  • Indiana Univ. Math. J., 67:1 (2018) pp. 429--469.

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