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On Initial-Boundary Value Problem of the Stochastic Heat Equation in Lipschitz Cylinders

Author

Listed:
  • Tongkeun Chang

    (Yonsei University)

  • Kijung Lee

    (Ajou University)

  • Minsuk Yang

    (Yonsei University)

Abstract

We consider the initial boundary value problem of the non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random noises. The space boundary is Lipschitz, and we impose nonzero condition on the parabolic boundary. We prove a regularity result by finding appropriate spaces for solutions and pre-assigned data in the problem. We use a collection of tools from potential theory, harmonic analysis, and probability. Some lemmas are as important as the main theorem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:26:y:2013:i:4:d:10.1007_s10959-012-0444-1
    DOI: 10.1007/s10959-012-0444-1
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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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