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Preprint (Vorabdruck) zugänglich unter
Interior regularity for free and constrained local minimizers of variational integrals under general growth and ellipticity conditions
URN: urn:nbn:de:bsz:291-scidok-43772
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4377/
pdf-Format:
Dokument 1.pdf (324 KB)
Institut:
Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer:
51
Sprache:
Englisch
Erstellungsjahr:
2002
Publikationsdatum:
01.12.2011
Kurzfassung auf Englisch:
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.
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