Please use this identifier to cite or link to this item: doi:10.22028/D291-26298
Title: Lavrentiev phenomenon, relaxation and some regularity results for anisotropic functionals
Author(s): Bildhauer, Michael
Fuchs, Martin
Language: English
Year of Publication: 2004
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: We study local minimizers of anisotropic variational integrals of the form J[u]=\int_{\Omega}f(\cdot,\nabla u)dx with integrand f satisfying a (p,\bar{q})-growth condition w.r.t. \nabla u and with D_{P}f(x,P) satisfying a Lipschitz condition w.r.t. x\in\Omega. If the Lavrentiev gap functional \mathcal{L} relative to J vanishes for all balls B_{R}\Subset\Omega and if \bar{q}<p(1+1/), then (partial) C^{1,\alpha}-regularity holds. Moreover, the bound on the exponents can be replaced by \bar{q}<p+1 provided we study locally bounded minimizers. We also investigate the relaxation of global minimization problems and discuss the regularity of the corresponding solutions. The importance of the condition \mathcal{L}\equiv0 was recently discovered by Esposito, Leonetti and Mingione in [ELM], where besides other results the higher integrability of the gradient is proved even under weaker assumptions than used here.
Link to this record: urn:nbn:de:bsz:291-scidok-44617
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 103
Date of registration: 10-Feb-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

Files for this record:
File Description SizeFormat 
preprint_103_04.pdf386,33 kBAdobe PDFView/Open

Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.