Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data
Probability
2021-03-16 v3
Abstract
We consider the obstacle problem with irregular barriers for semilinear elliptic equation involving measure data and operator corresponding to a general quasi-regular Dirichlet form. We prove existence and uniqueness of a solution as well as its representation as an envelope of a supersolution to some related partial differential equation. We also prove regularity results for the solution and the Lewy-Stampacchia inequality.
Keywords
Cite
@article{arxiv.1503.06402,
title = {Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data},
author = {Tomasz Klimsiak},
journal= {arXiv preprint arXiv:1503.06402},
year = {2021}
}