Summary
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.
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Krylov, N.V. AW n2 -theory of the Dirichlet problem for SPDEs in general smooth domains. Probab. Th. Rel. Fields 98, 389–421 (1994). https://doi.org/10.1007/BF01192260
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DOI: https://doi.org/10.1007/BF01192260