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On the \(L_q(L_p)\)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains. (English) Zbl 1309.60067

This paper improves the results in [P. A. Cioica et al., Stud. Math. 207, No. 3, 197–234 (2011; Zbl 1250.60026)], and the present article studies regularity of solutions for linear stochastic parabolic equations with zero Dirichlet boundary conditions on bounded Lipschitz domains. Namely, the authors establish Hölder regularity in time and Besov regularity in the spatial variable. The techniques used are due to Krylov, and co-authors, who introduced and studied weighted stochastic Sobolev spaces (cf. [N. V. Krylov, J. Funct. Anal. 183, No. 1, 1–41 (2001; Zbl 0980.60091)]).

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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