Please use this identifier to cite or link to this item: doi:10.22028/D291-26349
Title: Higher integrability of the gradient for vectorial minimizers of decomposable variational integrals
Author(s): Bildhauer, Michael
Fuchs, Martin
Language: English
Year of Publication: 2006
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: We consider local minimizers u:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{N} of variational integrals I[u]:=\int_{\Omega}F(\nabla u)dx, where F is of anisotropic (p,q)-growth with exponents 1<p\leq q<\infty. If F is in a certain sense decomposable, we show that the dimensionless restriction q\leq2p+2 together with the local boundedness of u implies local integrability of \nabla u for all exponents t\leq p+2. More precisely, the initial exponents for the integrability of the partial derivatives can be increased by two, at least locally. If n = 2, then we use these facts to prove C^{1,\alpha}-regularity of u for any exponents 2\leq p\leq q.
Link to this record: urn:nbn:de:bsz:291-scidok-46739
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 186
Date of registration: 13-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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