Liouville type results for a nonlocal obstacle problem
Résumé
This paper is concerned with qualitative properties of solutions to nonlocal reaction-diffusion equations of the form
$$ \int_{\mathbb{R}^N\setminus K} J(x-y)\,\big( u(y)-u(x) \big)\,\D y+f(u(x))=0, \quad x\in\R^N\setminus K,$$
set in a perforated open set $\mathbb{R}^N\setminus K$, where $K\subset\mathbb{R}^N$ is a bounded compact ``obstacle" and $f$ is a bistable nonlinearity. When $K$ is convex, we prove some Liouville-type results for solutions satisfying some asymptotic limiting conditions at infinity. We also establish a robustness result, assuming slightly relaxed conditions on $K$.
Origine : Fichiers produits par l'(les) auteur(s)
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