@article{EJP2478,
author = {Petru Cioica and Kyeong-Hun Kim and Kijung Lee and Felix Lindner},
title = {On the $L_q(L_p)$-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {18},
year = {2013},
keywords = {Stochastic partial differential equation; Lipschitz domain; \$L_q(L_p)\$-theory; weighted Sobolev space; Besov space; quasi-Banach space; embedding theorem; H\{\\"o\}lder regularity in time; nonlinear approximation; wavelet; adaptive numerical method},
abstract = {We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $\mathcal{O}\subset \mathbb{R}^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of stochastic parabolic weighted Sobole spaces $\mathfrak{H}^{\gamma,q}_{p,\theta}(\mathcal{O},T)$. The summability parameters $p$ and $q$ in space and time may differ. Existence and uniqueness of solutions in these spaces is established and the Hölder regularity in time is analysed. Moreover, we prove a general embedding of weighte $L_p(\mathcal{O})$-Sobolev spaces into the scale o Besov spaces $B^\alpha_{\tau,\tau}(\mathcal{O})$, $1/\tau=\alpha/d+1/p$, $\alpha>0$. This leads to a Hölder-Besov regularity result for the solution process. The regularity in this Besov scale determines the order of convergence that can be achieved by certain nonlinear approximation schemes.},
pages = {no. 82, 1-41},
issn = {1083-6489},
doi = {10.1214/EJP.v18-2478},
url = {http://ejp.ejpecp.org/article/view/2478}}