Liouville type results for a nonlocal obstacle problem

Julien Brasseur, Jérôme Coville, François Hamel, Enrico Valdinoci

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
JournalProceedings of the London Mathematical Society
Volume119
Issue number2
Early online date7 Feb 2019
DOIs
Publication statusPublished - Aug 2019

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Nonlocal Problems
Obstacle Problem
Nonlocal Equations
Qualitative Properties
Reaction-diffusion Equations
Open set
Limiting
Infinity
Nonlinearity
Robustness
Form

Cite this

Brasseur, Julien ; Coville, Jérôme ; Hamel, François ; Valdinoci, Enrico. / Liouville type results for a nonlocal obstacle problem. In: Proceedings of the London Mathematical Society. 2019 ; Vol. 119, No. 2. pp. 291-328.
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Liouville type results for a nonlocal obstacle problem. / Brasseur, Julien; Coville, Jérôme; Hamel, François; Valdinoci, Enrico.

In: Proceedings of the London Mathematical Society, Vol. 119, No. 2, 08.2019, p. 291-328.

Research output: Contribution to journalArticle

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