Dirichlet boundary value problems for elliptic operators with measure data: a probabilistic approach
Probability
2018-04-06 v1
Abstract
In this paper, we use probabilistic approach to prove that there exists a unique weak solution to the Dirichlet boundary value problem for second order elliptic equations whose coefficients are signed measures, and we will give a probabilistic representation of the solutions. This is the first time to study Dirichlet boundary value problems with this generality. The heat kernel estimates play a crucial role in our approach.
Cite
@article{arxiv.1804.01819,
title = {Dirichlet boundary value problems for elliptic operators with measure data: a probabilistic approach},
author = {Saisai Yang and Tusheng Zhang},
journal= {arXiv preprint arXiv:1804.01819},
year = {2018}
}