The singular set of minima of integral functionals

Abstract

In this paper we provide upper bounds for the Hausdorff dimension of the singular set of minima of general variational integrals ∫ ω 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 ω ⊂ ℝ n.