Archive for Rational Mechanics and Analysis

, Volume 180, Issue 3, pp 331–398

The Singular Set of Minima of Integral Functionals

Article

DOI: 10.1007/s00205-005-0402-5

Cite this article as:
Kristensen, J. & Mingione, G. Arch. Rational Mech. Anal. (2006) 180: 331. doi:10.1007/s00205-005-0402-5

Abstract

In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals https://static-content.springer.com/image/art%3A10.1007%2Fs00205-005-0402-5/MediaObjects/s00205-005-0402-5flb1.gif where F is suitably convex with respect to Dv and Hölder continuous with respect to (x,v). In particular, we prove that the Hausdorff dimension of the singular set is always strictly less than n, where https://static-content.springer.com/image/art%3A10.1007%2Fs00205-005-0402-5/MediaObjects/s00205-005-0402-5flb2.gif.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxford
  2. 2.Dipartimento di MatematicaUniversità di ParmaParma