An L p -theory of SPDEs on Lipschitz domains

Kyeong Hun Kim

doi:10.1007/s11118-008-9099-z

An L _p -theory of SPDEs on Lipschitz domains

Kyeong Hun Kim

Department of Mathematics

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

12 Citations (Scopus)

Abstract

Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary.

Original language	English
Pages (from-to)	303-326
Number of pages	24
Journal	Potential Analysis
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s11118-008-9099-z
Publication status	Published - 2008 Nov

Keywords

Lipschitz domains
Stochastic partial differential equations
Weighted Sobolev spaces

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/s11118-008-9099-z

Cite this

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title = "An L p -theory of SPDEs on Lipschitz domains",

abstract = "Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and H{\"o}lder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary.",

keywords = "Lipschitz domains, Stochastic partial differential equations, Weighted Sobolev spaces",

author = "Kim, {Kyeong Hun}",

note = "Funding Information: Acknowledgement This work was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-331-C00040).",

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AB - Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary.

KW - Lipschitz domains

KW - Stochastic partial differential equations

KW - Weighted Sobolev spaces

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