Article Dans Une Revue Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis) Année : 2017

A one-dimensional symmetry result for a class of nonlocal semilinear equations in the plane

Résumé

We consider entire solutions to Lu = f (u) in R 2 , where L is a nonlocal operator with translation invariant, even and compactly supported kernel K. Under different assumptions on the operator L, we show that monotone solutions are necessarily one-dimensional. The proof is based on a Liouville type approach. A variational characterization of the stability notion is also given, extending our results in some cases to stable solutions.

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hal-01174183 , version 1 (08-07-2015)

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François Hamel, Xavier Ros-Oton, Yannick Sire, Enrico Valdinoci. A one-dimensional symmetry result for a class of nonlocal semilinear equations in the plane. Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis), 2017, 34 (2), pp.469-482. ⟨10.1016/j.anihpc.2016.01.001⟩. ⟨hal-01174183⟩
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