Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

Details Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

2010-11-08

arxiv.org/abs/1011.1814v1

Mathematics

Probability

32 pages, 3 figures

Scientific paper

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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