Strong Solution of Backward Stochastic Partial Differential Equations in $C^2$ Domains

Details Strong Solution of Backward Stochastic Partial Differential Equations in $C^2$ Domains Strong Solution of Backward Stochastic Partial Differential Equations in $C^2$ Domains

2010-06-11

arxiv.org/abs/1006.2185v1

Mathematics

Probability

26 pages

Scientific paper

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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