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 hdl:20.500.11880/26420 http://dx.doi.org/10.22028/D291-26364 |
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 |
Files for this record:
File | Description | Size | Format | |
---|---|---|---|---|
preprint_202_07.pdf | 253,78 kB | Adobe PDF | View/Open |
Items in SciDok are protected by copyright, with all rights reserved, unless otherwise indicated.