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

Laurent Veron; Huyuan Chen

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arXiv · 1902.04806

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

Laurent Veron·Huyuan Chen

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Abstract

We study existence and stability of solutions of (E 1) --$\Delta$u + $\mu$ |x| 2 u + g(u) = $\nu$ in $\Omega$, u = 0 on $\partial$$\Omega$, where $\Omega$ is a bounded, smooth domain of R N , N $\ge$ 2, containing the origin, $\mu$ $\ge$ -- (N --2) 2 4 is a constant, g is a nondecreasing function satisfying some integral growth assumption and $\nu$ is a Radon measure on $\Omega$. We show that the situation differs according $\nu$ 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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Laurent Veron, Huyuan Chen. 2019-02-13. Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data. https://arxiv.org/abs/1902.04806

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