Boundary Value Problems with Measures for Elliptic Equations with Singular Potentials

Laurent Veron

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arXiv · 1002.4978

Boundary Value Problems with Measures for Elliptic Equations with Singular Potentials

Laurent Veron

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Abstract

We study the boundary value problem with Radon measures for nonnegative solutions of $-Δu+Vu=0$ in a bounded smooth domain $\Gw$, when $V$ is a locally bounded nonnegative function. Introducing some specific capacity, we give sufficient conditions on a Radon measure $\gm$ on $\prt\Gw$ so that the problem can be solved. We study the reduced measure associated to this equation as well as the boundary trace of positive solutions.

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Laurent Veron. 2010-02-26. Boundary Value Problems with Measures for Elliptic Equations with Singular Potentials. https://arxiv.org/abs/1002.4978

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