Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data

2019/02/13 by Veron, Laurent, Chen, Huyuan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.04806

Abstract

We study existence and stability of solutions of (E 1) --Δu + μ |x| 2 u + g(u) = ν in Ω, u = 0 on ∂Ω, where Ω is a bounded, smooth domain of R N , N ≥ 2, containing the origin, μ ≥ -- (N --2) 2 4 is a constant, g is a nondecreasing function satisfying some integral growth assumption and ν is a Radon measure on Ω. We show that the situation differs according ν is diffuse or concentrated at the origin. When g is a power we introduce a capacity framework to find necessary and sufficient condition for solvability.

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