Liouville type results for a nonlocal obstacle problem

Julien Brasseur, Jérôme Coville, François Hamel, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


This paper is concerned with qualitative properties of solutions to nonlocal reaction–diffusion equations of the form ∫ R N/K J(x-y)(u(y)-u(x))dy+f(u(x))=0, x∈R N/K set in a perforated open set R N/K , where K ⊂ 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.

Original languageEnglish
Pages (from-to)291-328
Number of pages38
JournalProceedings of the London Mathematical Society
Issue number5
Early online date7 Feb 2019
Publication statusPublished - Aug 2019


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