Please use this identifier to cite or link to this item: doi:10.22028/D291-26364
Title: Variational integrals of splitting-type : higher integrability under general growth conditions
Author(s): Bildhauer, Michael
Fuchs, Martin
Language: English
Year of Publication: 2007
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: Besides other things we prove that if u\in L_{loc}^{\infty}(\Omega;\mathbb{R}^{M}),\Omega\subset\mathbb{R}^{n}, locally minimizes the energy \int_{\Omega}\left[a(\left|\tilde{\nabla}u\right|)+b(\left|\partial_{n}u\right|)\right]dx, \tilde{\nabla}:=(\partial_{1},...,\partial_{n-1}), with N-functions a\leq b having the \Delta_{2}-property, then \left|\partial_{n}u\right|^{2}b(\left|\partial_{n}u\right|)\in L_{loc}^{1}(\Omega). Moreover, the condition b(t)\leq constt^{2}a(t^{2}) (*) for all large values of t implies \left|\tilde{\nabla}u\right|^{2}a(\left|\tilde{\nabla}u\right|)\in L_{loc}^{1}(\Omega). If n = 2, then these results can be improved up to \left|\nabla u\right|\in L_{loc}^{s}(\Omega) for all s<\infty without the hypothesis (*). If n\geq3 together with M = 1, then higher integrability for any exponent holds under more restrictive assumptions than (*).
Link to this record: urn:nbn:de:bsz:291-scidok-47321
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 202
Date of registration: 20-Mar-2012
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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