Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 199-214

PARTIAL REGULARITY FOR HIGHER ORDER VARIATIONAL PROBLEMS UNDER ANISOTROPICGROWTH CONDITIONS

Darya Apushkinskaya and Martin Fuchs

Universität des Saarlandes, Fachbereich 6.1 Mathematik
Postfach 15 11 50, D-66041 Saarbrücken, Germany; darya 'at' math.uni-sb.de

Universität des Saarlandes, Fachbereich 6.1 Mathematik
Postfach 15 11 50, D-66041 Saarbrücken, Germany; fuchs 'at' math.uni-sb.de

Abstract. We prove a partial regularity result for local minimizers u : Rⁿ \supset\Omega\to R^M of the variational integral J(u,\Omega) = \int_Omega f(\nabla^ku) 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 for the case n \geq 3 of the regularity theorem obtained in [BF2].

2000 Mathematics Subject Classification: Primary 49N60.

Key words: Variational problems of higher order, nonstandard growth, regularity of minimizers.

Reference to this article: D. Apushkinskaya and M. Fuchs: Partial regularity for higher order variational problems under anisotropic growth conditions. Ann. Acad. Sci. Fenn. Math. 32 (2007), 199-214.

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