Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
Volume 207 / 2011
Studia Mathematica 207 (2011), 197-234
MSC: Primary 60H15; Secondary 46E35, 65C30.
DOI: 10.4064/sm207-3-1
Abstract
We use the scale of Besov spaces , 1/\tau=\alpha/d+1/p, \alpha>0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains \mathcal{O}\subset\mathbb{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.
