Archive for Rational Mechanics and Analysis

, Volume 180, Issue 3, pp 331–398

The Singular Set of Minima of Integral Functionals


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


In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals 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

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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

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