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 hdl:20.500.11880/26405 http://dx.doi.org/10.22028/D291-26349 |
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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preprint_186_06.pdf | 215,25 kB | Adobe PDF | View/Open |
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