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A \(W_ 2^ n\)-theory of the Dirichlet problem for SPDEs in general smooth domains. (English) Zbl 0794.60062

Stochastic partial differential equations in smooth domains are considered in functional spaces of Sobolev type. The spaces are defined with the help of certain weights, which allow the derivatives of functions from these spaces to blow up near the boundary. Existence and uniqueness theorems are obtained.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
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