1. Boundary value problems with measures for elliptic equations with singular potentials
- Author
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Cecilia S. Yarur, Laurent Veron, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Departamento de Matematicas y CC (Departamento de Matematicas y CC), Universidad de Santiago de Chile [Santiago] (USACH), ECOS-Sud program C08E04. Fondecyt 1070125, and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS) more...
- Subjects
Poisson potential ,Borel measures ,Harnack inequalities ,Poisson kernel ,Boundary (topology) ,01 natural sciences ,Measure (mathematics) ,Domain (mathematical analysis) ,symbols.namesake ,Capacities ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Boundary value problem ,0101 mathematics ,Mathematics ,35J25 ,35J10 ,28A12 ,31C15 ,31C35 ,35C15 ,010102 general mathematics ,Mathematical analysis ,010101 applied mathematics ,Bounded function ,Radon measure ,symbols ,Laplacian ,Singularities ,Laplace operator ,Analysis ,Analysis of PDEs (math.AP) - Abstract
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. V\'eron concerning the vanishing set of the Poisson kernel of $L_V$ for an important class of potentials $V$., Comment: Contient un Appendice d'A. Ancona intitul\'e A necessary condition for the fine regularity of a boundary point with respect to a Schr\"odinger equation more...
- Published
- 2012
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