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2011 A $W^1_2$-Theory of Stochastic Partial Differential Systems of Divergence Type on $C^1$ Domains
Lee Kijung, Kim Kyeong-Hun
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Electron. J. Probab. 16: 1296-1317 (2011). DOI: 10.1214/EJP.v16-913

Abstract

In this paper we study the stochastic partial differential systems of divergence type with $\mathcal{C}^1$ space domains in $\mathbb{R}^d$. 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.

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Lee Kijung. Kim Kyeong-Hun. "A $W^1_2$-Theory of Stochastic Partial Differential Systems of Divergence Type on $C^1$ Domains." Electron. J. Probab. 16 1296 - 1317, 2011. https://doi.org/10.1214/EJP.v16-913

Information

Accepted: 7 July 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1225.60106
MathSciNet: MR2827460
Digital Object Identifier: 10.1214/EJP.v16-913

Subjects:
Primary: 60H15
Secondary: 35R60

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