Boundary value problems with measures for elliptic equations with singular potentials

We study the boundary value problem with Radon measures for nonnegative solutions of L(V)u := -Delta u + Vu = 0 in a bounded smooth domain Omega, when V is a locally bounded nonnegative function. Introducing some specific capacity, we give sufficient conditions on a Radon measure mu on a partial derivative Omega 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 Appendix A A. Ancona solves a question raised by M. Marcus and L. Veron concerning the vanishing set of the Poisson kernel of L v for an important class of potentials V. (C) 2011 Elsevier Inc. All rights reserved.