Spatial Besov regularity for stochastic partial
differential equations on Lipschitz domains
Studia Mathematica, Tome 207 (2011) no. 3, pp. 197-234
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We use the scale of Besov spaces $B^\alpha_{\tau,\tau}(\mathcal{O})$, $1/\tau=\alpha/d+1/p$, $\alpha>0$, $p$ fixed, to study the spatial regularity of solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains $\mathcal{O}\subset\mathbb{R}$. 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.
Keywords:
scale besov spaces alpha tau tau mathcal tau alpha alpha fixed study spatial regularity solutions linear parabolic stochastic partial differential equations bounded lipschitz domains mathcal subset mathbb besov smoothness determines order convergence achieved nonlinear approximation schemes proofs based combination weighted sobolev estimates characterizations besov spaces wavelet expansions
Affiliations des auteurs :
Petru A. Cioica 1 ; Stephan Dahlke 1 ; Stefan Kinzel 1 ; Felix Lindner 2 ; Thorsten Raasch 3 ; Klaus Ritter 4 ; René L. Schilling 2
@article{10_4064_sm207_3_1,
author = {Petru A. Cioica and Stephan Dahlke and Stefan Kinzel and Felix Lindner and Thorsten Raasch and Klaus Ritter and Ren\'e L. Schilling},
title = {Spatial {Besov} regularity for stochastic partial
differential equations on {Lipschitz} domains},
journal = {Studia Mathematica},
pages = {197--234},
publisher = {mathdoc},
volume = {207},
number = {3},
year = {2011},
doi = {10.4064/sm207-3-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm207-3-1/}
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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 SP - 197 EP - 234 VL - 207 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm207-3-1/ DO - 10.4064/sm207-3-1 LA - en ID - 10_4064_sm207_3_1 ER -
%0 Journal Article %A Petru A. Cioica %A Stephan Dahlke %A Stefan Kinzel %A Felix Lindner %A Thorsten Raasch %A Klaus Ritter %A René L. Schilling %T Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains %J Studia Mathematica %D 2011 %P 197-234 %V 207 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm207-3-1/ %R 10.4064/sm207-3-1 %G en %F 10_4064_sm207_3_1
Petru A. Cioica; Stephan Dahlke; Stefan Kinzel; Felix Lindner; Thorsten Raasch; Klaus Ritter; René L. Schilling. Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains. Studia Mathematica, Tome 207 (2011) no. 3, pp. 197-234. doi: 10.4064/sm207-3-1
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