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W2,p-solutions of parabolic SPDEs in general domains

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  • Du, Kai

Abstract

The Dirichlet problem for a class of stochastic partial differential equations is studied in Sobolev spaces. The existence and uniqueness result is proved under certain compatibility conditions that ensure the finiteness of Lp(Ω×(0,T),W2,p(G))-norms of solutions. The Hölder continuity of solutions and their derivatives is also obtained by embedding.

Suggested Citation

  • Du, Kai, 2020. "W2,p-solutions of parabolic SPDEs in general domains," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 1-19.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:1-19
    DOI: 10.1016/j.spa.2018.12.015
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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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