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arXiv · 1705.01310

Boundary singularities of solutions to semilinear fractional equations

Phuoc-Tai Nguyen·Laurent Veron·Laurent Eron
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Abstract

We prove the existence of a solution of (--$\Delta$) s u + f (u) = 0 in a smooth bounded domain $\Omega$ with a prescribed boundary value $\mu$ 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 $\mu$ is a Dirac mass, we prove the existence of several critical exponents p.

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Phuoc-Tai Nguyen, Laurent Veron, Laurent Eron. 2017-05-03. Boundary singularities of solutions to semilinear fractional equations. https://arxiv.org/abs/1705.01310

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