Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains

作者：Cioica Petru A^*; Dahlke Stephan; Kinzel Stefan; Lindner Felix; Raasch Thorsten; Ritter Klaus; Schilling Rene L

来源：Studia Mathematica, 2011, 207(3): 197-234.

DOI：10.4064/sm207-3-1

• stochastic partial differential equation
• Besov space
• Lipschitz domain
• wavelet
• weighted Sobolev space
• nonlinear approximation
• adaptive numerical scheme

We use the scale of Besov spaces B-tau,tau(alpha)(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 O subset of 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 Soholev estimates and characterizations of Besov spaces by wavelet expansions.

• 出版日期2011