Semilinear fractional elliptic equations with gradient nonlinearity involving measures

2013/08/30 by Chen, Huyuan, Veron, Laurent · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1308.6720

Abstract

We study the existence of solutions to the fractional elliptic equation (E1) (-Δ)^αu+εg(|∇ u|)=ν in a bounded regular domain Ω of \R^N (N≥2), subject to the condition (E2) u=0 in Ω^c, where ε=1 or -1, (-Δ)^α denotes the fractional Laplacian with α∈(1/2,1), ν is a Radon measure and g:\R₊↦\R₊ is a continuous function. We prove the existence of weak solutions for problem (E1)-(E2) when g is subcritical. Furthermore, the asymptotic behavior and uniqueness of solutions are described when ν is Dirac mass, g(s)=s^p, p≥ 1 and ε=1.

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