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Journal Articles Mathematics in Engineering Year : 2019

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

Huyuan Chen
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Laurent Veron

Abstract

We study existence and stability of solutions of (E 1) −∆u + 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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Dates and versions

hal-02013601 , version 1 (11-02-2019)
hal-02013601 , version 2 (02-04-2019)

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Huyuan Chen, Laurent Veron. Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data. Mathematics in Engineering, 2019, 1 (3), pp.391-418. ⟨10.3934/mine.2019.3.391⟩. ⟨hal-02013601v2⟩
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