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 $B^\alpha_{\tau,\tau}(\mathcal{O})$, $1/\tau=\alpha/d+1/p$, $\alpha>0$, $p$ 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.
