Dirichlet boundary value problems for elliptic operators with measure data: a probabilistic approach

Saisai Yang; Tusheng Zhang

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arXiv · 1804.01819

Dirichlet boundary value problems for elliptic operators with measure data: a probabilistic approach

Saisai Yang·Tusheng Zhang

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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.

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BibTeX RIS

Saisai Yang, Tusheng Zhang. 2018-04-05. Dirichlet boundary value problems for elliptic operators with measure data: a probabilistic approach. https://arxiv.org/abs/1804.01819

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