Please use this identifier to cite or link to this item: doi:10.22028/D291-26331
Title: New regularity theorems for non-autonomous anisotropic variational integrals
Author(s): Breit, Dominic
Language: English
Year of Publication: 2009
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: In the calculus of variations one prominent problem is minimizing anisotropic integrals with a (p,q)-elliptic density F:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{N}. The best known sufficient bound for regularity of solutions is q < p (n + 2)/n. On the other hand, if we allow an additional x-dependence of the density we have the much weaker result q < p (n + 1)/n. If one additionally imposes the local boundedness of the minimizer, then these bounds can be improved to q < p+2 and q < p + 1. In this paper we give natural assumptions for F closing the gap between the autonomous and non-autonomous situation.
Link to this record: urn:nbn:de:bsz:291-scidok-47749
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 241
Date of registration: 8-Mar-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_241_09.pdf256,84 kBAdobe PDFView/Open

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