Spatial Besov regularity for semilinear stochastic partial differential equations on bounded Lipschitz domains

被引：26

作者：

Cioica, Petru A. ^{[1
]}

Dahlke, Stephan ^{[1
]}

机构：

[1] Univ Marburg, FB Math & Informat, D-35032 Marburg, Germany

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2012年 / 89卷 / 18期

关键词：

semilinear stochastic partial differential equation; Besov space; weighted Sobolev space; nonlinear approximation; wavelet expansion; ADAPTIVE WAVELET METHODS; SPACES;

D O I：

10.1080/00207160.2011.631530

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the spatial regularity of semilinear parabolic stochastic partial differential equations on bounded Lipschitz domains O subset of R-d in the scale B-tau,tau(alpha) (O), 1/tau = alpha/d + 1/p, p >= 2 fixed. The Besov smoothness in this scale determines the order of convergence that can be achieved by adaptive numerical algorithms and other nonlinear approximation schemes. The proofs are performed by establishing weighted Sobolev estimates and combining them with wavelet characterizations of Besov spaces.

引用

页码：2443 / 2459

页数：17

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