W2,p-solutions of parabolic SPDEs in general domains

Kai Du

Stochastic Processes and their Applications, 2020, vol. 130, issue 1, 1-19

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.

Keywords: Stochastic partial differential equations; Dirichlet problem; Lp estimates; Compatibility conditions; Unbounded domains (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:1:p:1-19

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DOI: 10.1016/j.spa.2018.12.015

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