Schrödinger equations with smooth measure potential and general measure data. (May 2022)

• Record Type: Journal Article
• Authors: Klimsiak, Tomasz
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: primary 35J10 60J45 -- secondary 35B25 35J08 31C25 47G20; Schrödinger operator -- Smooth measure -- Singular potential -- Dirichlet form -- Markov process -- Green function -- Additive functional; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112774
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study equations driven by Schrödinger operators consisting of a self-adjoint Dirichlet operator and a singular potential, which belongs to a class of positive Borel measures absolutely continuous with respect to a capacity generated by the operator. In particular, we cover positive potentials exploding on a set of capacity zero. The right-hand side of equations is allowed to be a general bounded Borel measure. The class of self-adjoint Dirichlet operators is quite large. Examples include integro-differential operators with the local part of divergence form. We give a necessary and sufficient condition for the existence of a solution and prove some regularity and stability results.