Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups

Chuan-Zhong Chen; Wei Sun; Jing Zhang

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arXiv · 1407.4185

Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups

Chuan-Zhong Chen·Wei Sun·Jing Zhang

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Abstract

In this paper, we use a probabilistic approach to show that there exists a unique, bounded continuous solution to the Dirichlet boundary value problem for a general class of second order non-symmetric elliptic operators $L$ with singular coefficients, which does not necessarily have the maximum principle. The theory of Dirichlet forms and heat kernel estimates play a crucial role in our approach. A probabilistic representation of the non-symmetric semigroup $\{T_t\}_{t\ge 0}$ generated by $L$ is also given.

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BibTeX RIS

Chuan-Zhong Chen, Wei Sun, Jing Zhang. 2014-07-16. Probabilistic representations of solutions of elliptic boundary value problem and non-symmetric semigroups. https://arxiv.org/abs/1407.4185

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