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On the $L_q(L_p)$-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains

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1.	Title	Title of document	On the $L_q(L_p)$-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains
2.	Creator	Author's name, affiliation, country	Petru A. Cioica; Philipps-Universität Marburg; Germany
2.	Creator	Author's name, affiliation, country	Kyeong-Hun Kim; Korea University; Korea, Republic Of
2.	Creator	Author's name, affiliation, country	Kijung Lee; Ajou University; Korea, Republic Of
2.	Creator	Author's name, affiliation, country	Felix Lindner; TU Dresden; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	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
3.	Subject	Subject classification	60H15; 46E35; 35R60
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Deutsche Forschungsgemeinschaft (DFG); Philipps-Universität Marburg; National Research Foundation of Korea (NRF)
7.	Date	(YYYY-MM-DD)	2013-09-13
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2478
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2478
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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