Boundary singularities of solutions to semilinear fractional equations

Phuoc-Tai Nguyen (1) , Laurent Veron (2)

1 Departamento de Matemáticas [Santiago de Chile]
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Mots clés: s-harmonic functions; semilinear fractional equations; boundary trace

Domaines: Equations aux dérivées partielles [math.AP]

Phuoc-Tai Nguyen, Laurent Veron. Boundary singularities of solutions to semilinear fractional equations. 2017. ⟨hal-01516714v1⟩