A regularity result for a convex functional and bounds for the singular set
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the typewhere Ω is a bounded open set in , u∈(Ω; ), p> 1, n≥ 2 and N≥ 1. We use the technique of difference quotient without the usual assumption on the growth of the second derivatives of the function f. We apply this result to give a bound on the Hausdorff dimension of the singular set of minimizers.