Boundary singularities of solutions to semilinear fractional equationsReport as inadecuate

Boundary singularities of solutions to semilinear fractional equations - Download this document for free, or read online. Document in PDF available to download.

* 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 -



Related documents