A rigidity result for non-local semilinear equations

Alberto Farina (1) , Enrico Valdinoci

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We consider a possibly anisotropic integrodifferential semilinear equation, driven by a non-decreasing nonlinearity. We prove that if the solution grows less than the order of the operator at infinity, then it must be affine (possibly constant).

Domaines: Mathématiques [math]

Alberto Farina, Enrico Valdinoci. A rigidity result for non-local semilinear equations. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2017, 147 (5), pp.1009-1018. ⟨10.1017/S0308210516000391⟩. ⟨hal-03621416⟩