Boundary Value Problems with Measures for Elliptic Equations with Singular Potentials

We study the boundary value problem with Radon measures for nonnegative solutions of LVu:=-?u+Vu=0 in a bounded smooth domain ?, when V is a locally bounded nonnegative function. Introducing some specific capacity, we give sufficient conditions on a Radon measure ? on ? 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. Véron concerning the vanishing set of the Poisson kernel of LV for an important class of potentials V. © 2011 Elsevier Inc..