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* Corresponding author 1 PUC - Departamento de Matemáticas, Pontificia Universidad Católica de Chile 2 LMPT - Laboratoire de Mathématiques et Physique Théorique

Abstract : We prove the existence of a solution of −∆ s u + f u = 0 in a smooth bounded domain Ω with a prescribed boundary value µ in the class of positive Radon measures for a large class of continuous functions f satisfying a weak singularity condition expressed under an integral form. We study the existence of a boundary trace for positive moderate solutions. In the particular case where f u = u p and µ is a Dirac mass, we prove the existence of several critical exponents p.

Keywords : s-harmonic functions semilinear fractional equations boundary trace





Author: Phuoc-Tai Nguyen - Laurent Veron -

Source: https://hal.archives-ouvertes.fr/



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