A PROBABILISTIC APPROACH TO DIRICHLET PROBLEMS OF SEMILINEAR ELLIPTIC PDEs WITH SINGULAR COEFFICIENTS

• 成果类型: Article
• 署名作者: Zhang, Tusheng
• 署名单位: University of Manchester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP591
• 发表日期: 2011
• 页码: 1502-1527
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; symmetric markov-processes; time

摘要

In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic. The theory of Dirichlet processes and backward stochastic differential equations play a crucial role.