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Partial regularity for higher order variational problems under anisotropic growth conditions

By Darya Apushkinskaya and Martin Fuchs

Abstract

We prove a partial regularity result for local minimizers u : \mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{M} of the variational integral J(u,\Omega)=\int_{\Omega}f(\nabla^{k}u)dx, where k is any integer and f is a strictly convex integrand of anisotropic (p,q)-growth with exponents satisfying the condition q < p(1 + 2/n). This is some extension of the regularity theorem obtained in [BF2] for the case n = 2

Topics: variational problems of higher order, nonstandard growth, regularity of minimizers, Mathematics
Publisher: Fakultät 6 - Naturwissenschaftlich-Technische Fakultät I. Fachrichtung 6.1 - Mathematik
Year: 2005
OAI identifier: oai:scidok.sulb.uni-saarland.de:4627

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