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Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

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arxiv 1011.1814 v1 pith:4TUKTKPF submitted 2010-11-08 math.PR cs.NAmath.NA

Petru A. Cioica , Stephan Dahlke , Stefan Kinzel , Felix Lindner , Thorsten Raasch , Klaus Ritter , René L. Schilling This is my paper · ORCID
classification math.PRcs.NAmath.NA
keywords besovalphadifferentialdomainsequationslipschitzpartialregularity
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We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.

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