On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data
- Dipierro, Serena
- Soave, Nicola
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35J62 35J92 35J93 35B53
- Stability, symmetry results, classification of solution, reaction-diffusion equations, nonlocal equations
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.
- Indiana Univ. Math. J., 67:1 (2018) pp. 429--469.