Potential theory for elliptic systems
成果类型：
Article
署名作者：
Chen, ZQ; Zhao, Z
署名单位：
University of Missouri System; University of Missouri Columbia
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1996
页码：
293-319
关键词：
摘要：
The existence and uniqueness theorem is proved for solutions of the Dirichlet boundary value problems for weakly coupled elliptic systems on bounded domains. The elliptic systems are only assumed to have measurable coefficients and have singular coefficients for the lower-order terms. A probabilistic representation theorem for solutions of the Dirichlet boundary value problems is obtained by using the switched diffusion process associated with the system A strong positivity result for solutions of the Dirichlet boundary value problems is proved. Formulas expressing resolvents and kernel functions for the system by those of the component elliptic operators are also obtained.