*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 HÃ¶lder 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 $\Omega \subset R^n$.