Boundary singularities of solutions to semilinear fractional equations

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.
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Submitted on : Friday, January 19, 2018 - 1:45:05 PM
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  • HAL Id : hal-01516714, version 3
  • ARXIV : 1705.01310

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Phuoc-Tai Nguyen, Laurent Veron, Laurent Eron. Boundary singularities of solutions to semilinear fractional equations. Advanced Nonlinear Studies, Walter de Gruyter GmbH, In press. ⟨hal-01516714v3⟩

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