A W2n-theory of the Dirichlet problem for SPDEs in general smooth domains

N. V. Krylov

doi:10.1007/BF01192260

A W₂ⁿ-theory of the Dirichlet problem for SPDEs in general smooth domains

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

84 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	389-421
Number of pages	33
Journal	Probability Theory and Related Fields
Volume	98
Issue number	3
DOIs	https://doi.org/10.1007/BF01192260
State	Published - Sep 1994

Keywords

Mathematics Subject Classification (1991): 60H15, 35R60

Publisher link

10.1007/BF01192260

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title = "A W2n-theory of the Dirichlet problem for SPDEs in general smooth domains",

abstract = "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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AB - 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.

KW - Mathematics Subject Classification (1991): 60H15, 35R60

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