Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

2010/11/08 by Cioica, Petru A., Dahlke, Stephan, Kinzel, Stefan +4
#60H15 #65C30 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Secondary: 46E35

paper · doi:10.48550/arxiv.1011.1814

Abstract

We use the scale of Besov spaces B^α_τ,τ(O), α>0, 1/τ=α/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⊂ 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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