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

References

• Cioica , P. A. , Dahlke , S. , Kinzel , S. , Lindner , F. , Raasch , T. , Ritter , K. and Schilling , R. L. “ Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains ” . preprint (2010), submitted for publication. Available at http://www.dfg-spp1324.de/publications.php
   Google Scholar
• Cioica , P. A. , Dahlke , S. , Döhring , N. , Kinzel , S. , Lindner , F. , Raasch , T. , Ritter , K. and Schilling , R. L. “ Adaptive wavelet methods for elliptic stochastic partial differential equations ” . to appear in BIT, preprint (2011). Available at http://www.dfg-spp1324.de/publications.php
   Google Scholar
• Cohen , A. 2003 . Numerical Analysis of Wavelet Methods , Vol. 32 , Amsterdam : Elsevier . Studies in Mathematics and Its Applications
   Google Scholar
• Cohen , A. , Dahmen , W. and DeVore , R. A. 2001 . Adaptive wavelet methods for elliptic operator equations: Convergence rates . Math. Comput. , 70 : 27 – 75 .
   Web of Science ®Google Scholar
• Cohen , A. , Dahmen , W. and DeVore , R. A. 2002 . Adaptive wavelet methods II – Beyond the elliptic case . Found. Comput. Math. , 2 : 203 – 245 . (doi:10.1007/s102080010027)
   Web of Science ®Google Scholar
• Cohen , A. , Dahmen , W. and DeVore , R. A. 2003 . Adaptive wavelet methods for nonlinear variational problems . SIAM J. Numer. Anal. , 41 : 1785 – 1823 . (doi:10.1137/S0036142902412269)
   Web of Science ®Google Scholar
• Dahlke , S. 1999 . Besov regularity for elliptic boundary value problems in polygonal domains . Appl. Math. Lett. , 12 : 31 – 36 . (doi:10.1016/S0893-9659(99)00075-0)
   Web of Science ®Google Scholar
• Dahlke , S. 1999 . Besov regularity for interface problems . ZAMM Z. Angew. Math. Mech. , 79 : 383 – 388 . (doi:10.1002/(SICI)1521-4001(199906)79:6<383::AID-ZAMM383>3.0.CO;2-B)
   Web of Science ®Google Scholar
• Dahlke , S. 2003 . “ Besov regularity for the Neumann problem ” . In Function Spaces, Differential Operators, and Nonlinear Analysis, The Hans Triebel Anniversary Volume , Edited by: Haroske , D. , Runst , T. and Schmeisser , H.-J. 267 – 277 . Basel, Boston, Berlin : Birkhäuser .
   Google Scholar
• Dahlke , S. and DeVore , R. A. 1997 . Besov regularity for elliptic boundary value problems . Comm. Partial Differ. Equ. , 22 : 1 – 16 . (doi:10.1080/03605309708821252)
   Web of Science ®Google Scholar
• Dahlke , S. and Sickel , W. 2008 . “ Besov regularity for the Poisson equation in smooth and polyhedral cones ” . In Sobolev Spaces in Mathematics II, Applications in Analysis and Partial Differential Equations , Edited by: Maz'ya , V. 123 – 145 . Novosibirsk : Springer, jointly published with Tamara Rozhkovskaya Publisher . International Mathematical Series 9
   Google Scholar
• Dahlke , S. , Dahmen , W. and DeVore , R. A. 1997 . “ Nonlinear approximation and adaptive techniques for solving elliptic operator equations ” . In Multiscale Wavelet Methods for Partial Differential Equations , Edited by: Dahmen , W. , Kurdila , A. and Oswald , P. 237 – 283 . San Diego : Academic Press .
   Google Scholar
• Dahlke , S. , Dahmen , W. and Urban , K. 2002 . Adaptive wavelet methods for saddle point problems – optimal convergence rates . SIAM J. Numer. Anal. , 40 : 1230 – 1262 . (doi:10.1137/S003614290139233X)
   Web of Science ®Google Scholar
• Daubechies , I. 1992 . Ten Lectures on Wavelets , Philadelphia , PA : SIAM .
   Google Scholar
• DeVore , R. A. 1998 . Nonlinear approximation . Acta Numer. , 7 : 51 – 150 . (doi:10.1017/S0962492900002816)
   Google Scholar
• Dispa , S. 2003 . Intrinsic characterizations of Besov spaces on Lipschitz domains . Math. Nachr. , 260 : 21 – 33 . (doi:10.1002/mana.200310101)
   Web of Science ®Google Scholar
• Grisvard , P. 1985 . “ Elliptic Problems in Nonsmooth Domains ” . In Monographs and Studies in Mathematics 24 , Boston, London, Melbourne : Pitman .
   Google Scholar
• Grisvard , P. 1992 . “ Singularities in Boundary Value Problems ” . In Research Notes in Applied Mathematics 22 , Berlin : Springer .
   Google Scholar
• Hörmander , L. 1990 . “ The Analysis of Linear Partial Differential Operators I. Distribution Theory and Fourier Analysis ” . In , 2 , Berlin, Heidelberg, New York : Springer .
   Google Scholar
• Jerison , D. and Kenig , C. E. 1995 . The inhomogeneous Dirichlet problem in Lipschitz domains . J. Funct. Anal. , 130 : 161 – 219 . (doi:10.1006/jfan.1995.1067)
   Web of Science ®Google Scholar
• Kim , K.-H. 2008 . An Lp-theory of SPDEs on Lipschitz domains . Potential Anal. , 29 : 303 – 326 . (doi:10.1007/s11118-008-9099-z)
   Web of Science ®Google Scholar
• Kim , K.-H. A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains . preprint (2011), submitted for publication. Available at http://arxiv.org/abs/1109.4727
   Google Scholar
• Krylov , N. V. 1999 . “ An analytic approach to SPDEs ” . In Stochastic Partial Differential Equations. Six Perspectives , Edited by: Rozovskii , B. L. and Carmona , R. 185 – 242 . Providence , RI : American Mathematical Society . Mathematical Surveys and Monographs 64
   Google Scholar
• Kufner , A. 1980 . “ Weighted Sobolev Spaces ” . In Teubner-Texte zur Mathematik 31 , Leipzig : Teubner .
   Google Scholar
• Lindner , F. 2011 . “ Approximation and regularity of stochastic partial differential equations ” . Doctoral diss., TU Dresden, Aachen, Shaker
   Google Scholar
• Lototsky , S. V. 2000 . Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations . Methods Appl. Anal. , 7 : 195 – 204 .
   Google Scholar
• van Neerven , J. M.A.M. , Veraar , M. C. and Weis , L. 2008 . Stochastic evolution equations in UMD Banach spaces . J. Funct. Anal. , 255 : 940 – 993 . (doi:10.1016/j.jfa.2008.03.015)
   Web of Science ®Google Scholar
• Rychkov , V. S. 1999 . On restrictions and extensions of the Besov and Triebel–Lizorkin spaces with respect to Lipschitz domains . J. Lond. Math. Soc. , 60 : 237 – 257 . (doi:10.1112/S0024610799007723)
   Web of Science ®Google Scholar
• Triebel , H. 1995 . “ Interpolation Theory, Function Spaces, Differential Operators ” . In , 2 , Leipzig : Barth .
   Google Scholar
• Veraar , M. C. 2010 . Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations . J. Evol. Equ. , 10 : 85 – 127 . (doi:10.1007/s00028-009-0041-7)
   Web of Science ®Google Scholar