Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

A note on Liouville type results for a fractional obstacle problem

Abstract : This note is a synthesis of my reflexions on some questions that have emerged during the MATRIX event "Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type" concerning the qualitative properties of solutions to some non local reaction-diffusion equations of the form L[u](x) + f (u(x)) = 0, for x ∈ R n \ K, where K ⊂ R N is a bounded smooth compact "obstacle", L is non local operator and f is a bistable nonlinearity. When K is convex and the nonlocal operator L is a continuous operator of convolution type then some Liouville-type results for solutions satisfying some asymptotic limiting conditions at infinity have been recently established by Brasseur, Coville, Hamel and Valdinoci [4]. Here, we show that for a bounded smooth convex obstacle K, similar Liouville type results hold true when the operator L is the regional s-fractional Laplacian.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download

https://hal.inrae.fr/hal-02789001
Contributor : Migration Prodinra <>
Submitted on : Friday, June 5, 2020 - 4:29:53 AM
Last modification on : Monday, November 30, 2020 - 6:42:02 PM

File

Coville-Arxiv-2019_1.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

  • HAL Id : hal-02789001, version 1
  • PRODINRA : 463855

Collections

Citation

Jerome Coville. A note on Liouville type results for a fractional obstacle problem. 2019. ⟨hal-02789001⟩

Share

Metrics

Record views

22

Files downloads

35