Annales Academić Scientiarum Fennicć
Mathematica
Volumen 36, 2011, 279-289

SPLITTING-TYPE VARIATIONAL PROBLEMS WITH x-DEPENDENT EXPONENTS

Dominic Breit

Saarland University, Department of Mathematics
P.O. Box 15 11 50, 66041 Saarbrücken, Germany; Dominic.Breit 'at' math.uni-sb.de

Abstract. In this article we prove regularity results for locally bounded minimizers u : Rⁿ \supset \Omega \rightarrow R^N of functionals of the type

\int_\Omega [(1 + |\nabla₁u|²)^p(x)/2 + (1 + |\nabla₂u|²)^q(x)/2]dx

where p and q are Lipschitz-functions and \nabla u = (\nabla₁u,\nabla₂u) is an arbitrary decompositon of the gradient of u. Related functionals are the topic of the paper [Br3], but the situation here is not covered.

2000 Mathematics Subject Classification: Primary 49N60.

Key words: Variational problems of splitting-type, regularity of minimizers, nonautonomous functionals.

Reference to this article: D. Breit: Splitting-type variational problems with x-dependent exponents. Ann. Acad. Sci. Fenn. Math. 36 (2011), 279-289.

Full document as PDF file

doi:10.5186/aasfm.2011.3617