Please use this identifier to cite or link to this item:
doi:10.22028/D291-26202
Title: | Interior regularity for free and constrained local minimizers of variational integrals under general growth and ellipticity conditions |
Author(s): | Bildhauer, Michael Fuchs, Martin |
Language: | English |
Year of Publication: | 2002 |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
Abstract: | We consider strictly convex energy densities f:\mathbb{R}^{n}\rightarrow\mathbb{R} under nonstandard growth conditions. More precisely, we assume that for some constants \lambda, \Lambda and for all Z,Y\in\mathbb{R}^{n} the inequality \lambda(1+\left|Z\right|^{2})^{-\frac{\mu}{2}}\left|Y\right|^{2}\leq D^{2}f(Z)(Y,Y)\leq\Lambda(1+\left|Z\right|^{2})^{\frac{q-2}{2}}\left|Y\right|^{2} holds with exponents \mu\in\mathbb{R} and q>1. If u denotes a bounded local minimizer of the energy \int f(\nabla w)dx subject to a constraint of the form w\geq\psi a.e. with a given obstacle \psi\in C^{1,\alpha}(\Omega), then we prove local C^{1,\alpha}-regularity of u provided that q<4-\mu. This result substantially improves what is known up to now (see, for instance, [CH], [BFM], [FM]), even for the case of unconstrained local minimizers. |
Link to this record: | urn:nbn:de:bsz:291-scidok-43772 hdl:20.500.11880/26258 http://dx.doi.org/10.22028/D291-26202 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 51 |
Date of registration: | 1-Dec-2011 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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