Archive for Rational Mechanics and Analysis

, Volume 180, Issue 3, pp 331–398

The Singular Set of Minima of Integral Functionals


    • Mathematical InstituteUniversity of Oxford
  • Giuseppe Mingione
    • Dipartimento di MatematicaUniversità di Parma

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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