TIME-REVERSAL AND ELLIPTIC BOUNDARY VALUE PROBLEMS

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Zhang, Tusheng
• 署名单位: University of Washington; University of Washington Seattle; University of Manchester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP427
• 发表日期: 2009
• 页码: 1008-1043
• 关键词: symmetric markov-processes; coefficients; semigroups; Operators; forms

摘要

In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have the maximum principle. Our method is probabilistic. The time reversal of symmetric Markov processes and the theory of Dirichlet forms play a crucial role in our approach.