A W12 -theory of Stochastic Partial Differential Systems of Divergence type on C1 domains

Kyeong Hun Kim; Kijung Lee

doi:10.1214/EJP.v16-913

A W¹₂ -theory of Stochastic Partial Differential Systems of Divergence type on C¹ domains

Kyeong Hun Kim, Kijung Lee

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

4 Citations (Scopus)

Abstract

In this paper we study the stochastic partial differential systems of divergence type with C¹ space domains in R^d . Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.

Original language	English
Pages (from-to)	1296-1317
Number of pages	22
Journal	Electronic Journal of Probability
Volume	16
DOIs	https://doi.org/10.1214/EJP.v16-913
Publication status	Published - 2011 Jan 1

Keywords

Divergence type
Stochastic parabolic partial differential systems
Weighted Sobolev spaces

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/EJP.v16-913

Cite this

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title = "A W12 -theory of Stochastic Partial Differential Systems of Divergence type on C1 domains",

abstract = "In this paper we study the stochastic partial differential systems of divergence type with C1 space domains in Rd . Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.",

keywords = "Divergence type, Stochastic parabolic partial differential systems, Weighted Sobolev spaces",

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AU - Kim, Kyeong Hun

AU - Lee, Kijung

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N2 - In this paper we study the stochastic partial differential systems of divergence type with C1 space domains in Rd . Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.

AB - In this paper we study the stochastic partial differential systems of divergence type with C1 space domains in Rd . Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.

KW - Divergence type

KW - Stochastic parabolic partial differential systems

KW - Weighted Sobolev spaces

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DO - 10.1214/EJP.v16-913

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JF - Electronic Journal of Probability

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