# 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
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 $\Omega \subset R^n$.