Abstract
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.
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Supported by NSFC Grant #10325101, by Basic Research Program of China (973 Program) Grant # 2007CB814904, by the Science Foundation of the Ministry of Education of China Grant #200900071110001, by Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) (NO. IRT0912), and by WCU (World Class University) Program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (R31-2009-000-20007).
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Du, K., Tang, S. Strong solution of backward stochastic partial differential equations in C 2 domains. Probab. Theory Relat. Fields 154, 255–285 (2012). https://doi.org/10.1007/s00440-011-0369-0
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DOI: https://doi.org/10.1007/s00440-011-0369-0
Keywords
- Backward stochastic partial differential equations
- Strong solutions
- C 2 domains
- Weighted Sobolev spaces
Mathematics Subject Classification (2000)
- 60H15
- 35R60
- 93E20