Strong solution of backward stochastic partial differential equations in C2 domains

• 成果类型: Article
• 署名作者: Du, Kai; Tang, Shanjian
• 署名单位: Fudan University; Fudan University; Ajou University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0369-0
• 发表日期: 2012
• 页码: 255-285
• 关键词: adapted solution; CONTROLLABILITY

摘要

This paper is concerned with the strong solution to the Cauchy-Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the continuation method under fairly weak conditions on variable coefficients and C (2) domains. The problem is also considered in weighted Sobolev spaces which allow the derivatives of the solutions to blow up near the boundary. As applications, a comparison theorem is obtained and the semi-linear equation is discussed in the C (2) domain.