W2,p-solutions of parabolic SPDEs in general domains

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Du, Kai¹ 

[1] Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200438, Peoples R China

关键词: Stochastic partial differential equations;    Dirichlet problem;    L-P estimates;    Compatibility conditions;    Unbounded domains;   

DOI  :  10.1016/j.spa.2018.12.015

来源: Elsevier

【 摘 要 】

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 L-P(Omega x (0, T), W-2,W-P(G))-norms of solutions. The Holder continuity of solutions and their derivatives is also obtained by embedding. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free