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Pré-Publication, Document De Travail Année : 2010

Boundary value problems with measures for elliptic equations with singular potentials

Cecilia Yarur
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Résumé

We study the boundary value problem with Radon measures for nonnegative solutions of $L_Vu:=-\Delta u+Vu=0$ 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. In the appendix A. Ancona solves a question raised by M. Marcus and L. Véron concerning the vanishing set of the Poisson kernel of $L_V$ for an important class of potentials $V$.
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Dates et versions

hal-00499648 , version 1 (11-07-2010)
hal-00499648 , version 2 (13-07-2010)

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Laurent Veron, Cecilia Yarur. Boundary value problems with measures for elliptic equations with singular potentials. 2010. ⟨hal-00499648v2⟩
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