Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains

Petru A. Cioica, et al. "Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains." Studia Mathematica 207.3 (2011): 197-234. <http://eudml.org/doc/285442>.

@article{PetruA2011,
abstract = {We use the scale of Besov spaces $B^\{α\}_\{τ,τ\}()$, 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ 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 Sobolev estimates and characterizations of Besov spaces by wavelet expansions.},
author = {Petru A. Cioica, Stephan Dahlke, Stefan Kinzel, Felix Lindner, Thorsten Raasch, Klaus Ritter, René L. Schilling},
journal = {Studia Mathematica},
keywords = {stochastic partial differential equations; spatial Besov regularity},
language = {eng},
number = {3},
pages = {197-234},
title = {Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains},
url = {http://eudml.org/doc/285442},
volume = {207},
year = {2011},
}

TY - JOUR
AU - Petru A. Cioica
AU - Stephan Dahlke
AU - Stefan Kinzel
AU - Felix Lindner
AU - Thorsten Raasch
AU - Klaus Ritter
AU - René L. Schilling
TI - Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
JO - Studia Mathematica
PY - 2011
VL - 207
IS - 3
SP - 197
EP - 234
AB - We use the scale of Besov spaces $B^{α}_{τ,τ}()$, 1/τ = α/d + 1/p, α > 0, p fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains ⊂ 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 Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
LA - eng
KW - stochastic partial differential equations; spatial Besov regularity
UR - http://eudml.org/doc/285442
ER -