English

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.

Keywords

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}
}
R2 v1 2026-06-23T01:14:52.673Z