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Sobolev space theory of SPDEs with continuous or measurable leading coefficients

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  • Kim, Kyeong-Hun

Abstract

We study stochastic partial differential equations with variable coefficients defined on and bounded C1 domains. For equations with continuous leading coefficients we give existence and uniqueness results in Lq(Lp)-spaces, where it is allowed for the powers of summability with respect to space and time variables to be different. For equations with measurable leading coefficients we give unique solvability in Lp-spaces.

Suggested Citation

  • Kim, Kyeong-Hun, 2009. "Sobolev space theory of SPDEs with continuous or measurable leading coefficients," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 16-44, January.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:1:p:16-44
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    References listed on IDEAS

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    1. Kim, Kyeong-Hun, 2004. "On stochastic partial differential equations with variable coefficients in C1 domains," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 261-283, August.
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    Cited by:

    1. Konstantinos Spiliopoulos & Justin A. Sirignano & Kay Giesecke, 2013. "Fluctuation Analysis for the Loss From Default," Papers 1304.1420, arXiv.org, revised Feb 2015.
    2. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
    3. Kim, Ildoo & Kim, Kyeong-Hun, 2018. "A regularity theory for quasi-linear Stochastic PDEs in weighted Sobolev spaces," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 622-643.

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