DC Element | Wert | Sprache |
dc.contributor.author | Dahlke, Stephan | |
dc.contributor.author | Diening, Lars | |
dc.contributor.author | Hartmann, Christoph | |
dc.contributor.author | Scharf, Benjamin | |
dc.contributor.author | Weimar, Markus | |
dc.date.accessioned | 2021-12-23T16:19:28Z | - |
dc.date.available | 2021-12-23T16:19:28Z | - |
dc.date.issued | 2016 | |
dc.identifier.issn | 0362546X | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/13161 | - |
dc.description.abstract | In this paper, we are concerned with regularity analysis for solutions to nonlinear partial differential equations. Many important practical problems are related with the p-Laplacian. Therefore, we are particularly interested in the smoothness of solutions to the p-Poisson equation. For the full range of parameters 1 < p < infinity we investigate regularity estimates in the adaptivity scale B-tau(sigma) (L-tau(Omega)), 1/tau = sigma/d 1/p, of Besov spaces. The maximal smoothness a in this scale determines the order of approximation that can be achieved by adaptive and other nonlinear approximation methods. It turns out that, especially for solutions to p-Poisson equations with homogeneous Dirichlet boundary conditions on bounded polygonal domains, the Besov regularity is significantly higher than the Sobolev regularity which justifies the use of adaptive algorithms. This type of results is obtained by combining local Holder with global Sobolev estimates. In particular, we prove that intersections of locally weighted Hiilder spaces and Sobolev spaces can be continuously embedded into the specific scale of Besov spaces we are interested in. The proof of this embedding result is based on wavelet characterizations of Besov spaces. (C) 2015 Elsevier Ltd. All rights reserved. | |
dc.description.sponsorship | Deutsche Forschungsgemeinschaft DFGGerman Research Foundation (DFG) [DA 360/18-1, DA 360/19-1]; European Research Council ERCEuropean Research Council (ERC) [HDSP-CONTR-306274]; The authors like to thank the anonymous referee whose comments helped to improve the paper. In addition, the first, third, and fifth author gratefully acknowledge the support by Deutsche Forschungsgemeinschaft DFG (DA 360/18-1 and DA 360/19-1). Moreover, the fourth author has been supported by European Research Council ERC (Starting Grant HDSP-CONTR-306274). | |
dc.language.iso | en | |
dc.publisher | PERGAMON-ELSEVIER SCIENCE LTD | |
dc.relation.ispartof | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | |
dc.subject | approximation Wavelets | |
dc.subject | Besov spaces | |
dc.subject | BOUNDARY-VALUE-PROBLEMS | |
dc.subject | DOMAINS | |
dc.subject | ELLIPTIC-EQUATIONS | |
dc.subject | Holder spaces | |
dc.subject | Mathematics | |
dc.subject | Mathematics, Applied | |
dc.subject | Nonlinear and adaptive | |
dc.subject | p-Poisson equation | |
dc.subject | Regularity of solutions | |
dc.subject | TRIEBEL-LIZORKIN SPACES | |
dc.title | Besov regularity of solutions to the p-Poisson equation | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.na.2015.10.015 | |
dc.identifier.isi | ISI:000365186200019 | |
dc.description.volume | 130 | |
dc.description.startpage | 298 | |
dc.description.endpage | 329 | |
dc.contributor.orcid | 0000-0002-1850-7518 | |
dc.contributor.orcid | 0000-0002-0523-3079 | |
dc.contributor.orcid | 0000-0003-0283-8926 | |
dc.contributor.researcherid | G-4739-2015 | |
dc.identifier.eissn | 18735215 | |
dc.publisher.place | THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND | |
dcterms.isPartOf.abbreviation | Nonlinear Anal.-Theory Methods Appl. | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.orcid | 0000-0002-0523-3079 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | DiLa398 | - |