On the L-q(L-p)-regularity and Besov smoothness of stochastic parabolic equations on bounded Lipschitz domains
- Authors
- Cioica, Petru A.; Kim, Kyeong-Hun; Lee, Kijung; Lindner, Felix
- Issue Date
- 13-9월-2013
- Publisher
- UNIV WASHINGTON, DEPT MATHEMATICS
- Keywords
- Stochastic partial differential equation; Lipschitz domain; L-q(L-p)-theory; weighted Sobolev space; Besov space; quasi-Banach space; embedding theorem; Holder regularity in time; nonlinear approximation; wavelet; adaptive numerical method; square root of Laplacian operator
- Citation
- ELECTRONIC JOURNAL OF PROBABILITY, v.18, pp.1 - 41
- Indexed
- SCIE
SCOPUS
- Journal Title
- ELECTRONIC JOURNAL OF PROBABILITY
- Volume
- 18
- Start Page
- 1
- End Page
- 41
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/102162
- DOI
- 10.1214/EJP.v18-2478
- ISSN
- 1083-6489
- Abstract
- We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains O subset of R-d with both theoretical and numerical purpose. We use N.V. Krylov's framework of stochastic parabolic weighted Sobolev spaces h(p,theta)(gamma,q)(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 Holder regularity in time is analysed. Moreover, we prove a general embedding of weighted L-p(O)-Sobolev spaces into the scale of Besov spaces B-tau,tau(alpha) (O), 1/tau = alpha/d + 1/p, alpha > 0. This leads to a Holder-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.
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