Calculus of Variations and Geometric Measure Theory
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J. Kristensen - G. Mingione

The singular set of minima of integral functionals

created by mingione on 28 May 2005
modified on 06 Mar 2015

[BibTeX]

Published Paper

Inserted: 28 may 2005
Last Updated: 6 mar 2015

Journal: Arch. Ration. Mech. Anal.
Volume: 180
Number: 3
Pages: 331-398
Year: 2006
Links: paper

Abstract:

In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals \[ \int_{\Omega} F(x,v,Dv)\ dx\;, \] 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 $\Omega \subset R^n$.

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