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

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.
Type de document :
Pré-publication, Document de travail
2019
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https://hal.archives-ouvertes.fr/hal-02013601
Contributeur : Laurent Veron <>
Soumis le : lundi 11 février 2019 - 10:41:35
Dernière modification le : jeudi 14 février 2019 - 01:21:20

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Hardy Radon 13.pdf
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  • HAL Id : hal-02013601, version 1
  • ARXIV : 1902.04806

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Laurent Veron, Huyuan Chen. Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data. 2019. 〈hal-02013601〉

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