, Volume 180, Issue 3, pp 331-398
Date: 21 Oct 2005

The Singular Set of Minima of Integral Functionals

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Abstract

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 .

Communicated by V. Šverák