BOUNDARY VALUE PROBLEMS WITH MEASURES FOR ELLIPTIC EQUATIONS WITH SINGULAR POTENTIALS

Laurent Veron (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We study the boundary value problem with Radon measures for nonnegative solutions of $-\Delta u+Vu=0$ 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.

Mots clés: Laplacian; Poisson potential; capacities; singularities; Borel measures; Harnack inequalities.; Harnack inequalities

Domaines: Equations aux dérivées partielles [math.AP]

Laurent Veron. BOUNDARY VALUE PROBLEMS WITH MEASURES FOR ELLIPTIC EQUATIONS WITH SINGULAR POTENTIALS. 2010. ⟨hal-00460125⟩