Schr\"odinger equations with smooth measure potential and general measure data
Analysis of PDEs
2023-08-22 v2
Abstract
We study equations driven by Schr\"odinger 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.
Cite
@article{arxiv.1910.03717,
title = {Schr\"odinger equations with smooth measure potential and general measure data},
author = {Tomasz Klimsiak},
journal= {arXiv preprint arXiv:1910.03717},
year = {2023}
}