manuscripta mathematica

, Volume 126, Issue 1, pp 1–40

Partial regularity for minima of higher order functionals with p(x)-growth

Article

DOI: 10.1007/s00229-007-0147-6

Cite this article as:
Habermann, J. manuscripta math. (2008) 126: 1. doi:10.1007/s00229-007-0147-6

Abstract

For higher order functionals \(\int_\Omega f(x, \delta u(x), {D^m}u(x))\,dx\) with p(x)-growth with respect to the variable containing Dmu, we prove that Dmu is Hölder continuous on an open subset \(\Omega_0 \subset \Omega\) of full Lebesgue-measure, provided that the exponent function \(p : \Omega \to (1, \infty)\) itself is Hölder continuous.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Institute for MathematicsFriedrich-Alexander UniversityErlangenGermany