Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

• DOI: 10.48550/arxiv.1011.1814
• Publication Date: 2010-01-01
• Authors: Petru A. Cioica-L...; Stephan Dahlke; Stefan Kinzel; Felix Lindner; Thorsten Raasch; Klaus Ritter; René L. Schilling
• Keywords: Besov space; Smoothness

We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study spatial regularity solutions linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The smoothness determines order convergence that can be achieved by nonlinear approximation schemes. proofs are based a combination weighted Sobolev estimates and characterizations wavelet expansions.