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On stochastic partial differential equations with variable coefficients in C1 domains

Author

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  • Kim, Kyeong-Hun

Abstract

Stochastic partial differential equations with variable coefficients are considered in C1 domains. Existence and uniqueness results are given in Sobolev spaces with weights allowing the derivatives of the solutions to blow up near the boundary. The number of derivatives of the solution can be negative and fractional, and the coefficients of the equations are allowed to substantially oscillate or blow up near the boundary.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:112:y:2004:i:2:p:261-283
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    Citations

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    Cited by:

    1. Gerencsér, Máté & Gyöngy, István, 2019. "A Feynman–Kac formula for stochastic Dirichlet problems," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 995-1012.
    2. Kim, Kyeong-Hun, 2004. "Lq(Lp) theory and Hölder estimates for parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 313-330, December.
    3. Kyeong-Hun Kim, 2008. "L p -Theory of Parabolic SPDEs Degenerating on the Boundary of C 1 Domains," Journal of Theoretical Probability, Springer, vol. 21(1), pages 169-192, March.
    4. Krylov, N.V., 2009. "On divergence form SPDEs with VMO coefficients in a half space," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2095-2117, June.
    5. Kyeong-Hun Kim, 2014. "A Weighted Sobolev Space Theory of Parabolic Stochastic PDEs on Non-smooth Domains," Journal of Theoretical Probability, Springer, vol. 27(1), pages 107-136, March.
    6. Kim, Kyeong-Hun, 2014. "A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on C1-domains," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 440-474.
    7. Tongkeun Chang & Kijung Lee & Minsuk Yang, 2013. "On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders," Journal of Theoretical Probability, Springer, vol. 26(4), pages 1135-1164, December.
    8. Kim, Kyeong-Hun & Lee, Kijung, 2013. "A note on Wpγ-theory of linear stochastic parabolic partial differential systems," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 76-90.
    9. 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.
    10. Du, Kai, 2020. "W2,p-solutions of parabolic SPDEs in general domains," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 1-19.

    More about this item

    Keywords

    Stochastic partial differential equations Sobolev spaces with weights C1 domains;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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