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arXiv · 1207.4398

Existence and stability of solutions of general semilinear elliptic equations with measure data

Laurent Veron
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Abstract

We study existence and stability for solutions of $Lu+g(x; u) = ω$ in the closure of open set $Ω$ where L is a second order elliptic operator, $g$ a Caratheodory function and $ω$ a measure in $\barΩ$. We present a uni ed theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.

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Laurent Veron. 2012-08-31. Existence and stability of solutions of general semilinear elliptic equations with measure data. https://arxiv.org/abs/1207.4398

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