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On L p -theory of stochastic partial differential equations of divergence form in C1 domains
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  • Published: 05 July 2004

On L p -theory of stochastic partial differential equations of divergence form in C1 domains

  • Kyeong-Hun Kim1 

Probability Theory and Related Fields volume 130, pages 473–492 (2004)Cite this article

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Abstract.

Stochastic partial differential equations of divergence form are considered in C1 domains. Existence and uniqueness results are given in a Sobolev space with weights allowing the derivatives of the solutions to blow up near the boundary.

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Acknowledgments.

The author is sincerely grateful to Prof. N.V. Krylov for his valuable suggestions.

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Authors and Affiliations

  1. 127 Vincent Hall, University of Minnesota, Minneapolis, MN, 55455, USA

    Kyeong-Hun Kim

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  1. Kyeong-Hun Kim
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Correspondence to Kyeong-Hun Kim.

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Mathematics Subject Classification (2000): 60H15, 35R60

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Cite this article

Kim, KH. On L p -theory of stochastic partial differential equations of divergence form in C1 domains. Probab. Theory Relat. Fields 130, 473–492 (2004). https://doi.org/10.1007/s00440-004-0368-5

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  • Received: 21 October 2003

  • Revised: 16 March 2004

  • Published: 05 July 2004

  • Issue Date: December 2004

  • DOI: https://doi.org/10.1007/s00440-004-0368-5

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Keywords

  • Stochastic partial differential equations
  • Sobolev spaces with weights
  • C1 domains
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