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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Chen, Chuan-Zhong¹  Sun, Wei²  Zhang, Jing² 

[1] Hainan Normal Univ, Sch Math & Stat, Haikou 571158, Peoples R China

[2] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

关键词: Dirichlet boundary value problem;    Singular coefficient;    Non-symmetric semigroup;    Probabilistic representation;    Dirichlet form;    Heat kernel estimate;   

DOI  :  10.1016/j.jde.2015.08.034

来源: Elsevier

【 摘 要 】

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 >= 0) generated by L is also given. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free