%0 Journal Article
%T Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains
%A Petru A. Cioica
%A Stephan Dahlke
%A Stefan Kinzel
%A Felix Lindner
%A Thorsten Raasch
%A Klaus Ritter
%A Ren¨¦ L. Schilling
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1011.1814v1