Please use this identifier to cite or link to this item: doi:10.22028/D291-26194
Title: Partial regularity for a class of anisotropic variational integrals with convex hull property
Author(s): Bildhauer, Michael
Fuchs, Martin
Language: English
Year of Publication: 2001
Free key words: anisotropic growth
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: We consider integrands f:\mathbb{R}^{nN}\rightarrow\mathbb{R} which are of lower (upper) growth rate s\geq2(q>s) and which satisfy an additional structural condition implying the convex hull property, i.e. if the boundary data of a minimizer u:\Omega\rightarrow\mathbb{R}^{N} of the energy \int_{\Omega}f(\nabla u)dx respect a closed convex set K\subset\mathbb{R}^{N}, then so does u on the whole domain. We show partial C^{1,\alpha}-regularity of bounded local minimizers if q<min\{s+\frac{2}{3},s\frac{n}{n-2}\} and discuss cases in which the latter condition on the exponents can be improved. Moreover, we give examples of integrands which fit into our category and to which the results of Acerbi and Fusco [AF2] do not apply, in particular, we give some extensions to the subquadratic case.
Link to this record: urn:nbn:de:bsz:291-scidok-43579
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 38
Date of registration: 25-Nov-2011
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_38_01.pdf299,6 kBAdobe PDFView/Open

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