We use the scale of Besov spaces , 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ ℝ. 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-3-1,
author = {Petru A. Cioica and Stephan Dahlke and Stefan Kinzel and Felix Lindner and Thorsten Raasch and Klaus Ritter and Ren\'e L. Schilling},
title = {Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {197-234},
zbl = {1250.60026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-3-1}
}
Petru A. Cioica; Stephan Dahlke; Stefan Kinzel; Felix Lindner; Thorsten Raasch; Klaus Ritter; René L. Schilling. Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains. Studia Mathematica, Tome 204 (2011) pp. 197-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-3-1/