Published online by Cambridge University Press: 11 August 2009
In this paper we prove a regularityresult for local minimizers of functionals of the Calculus of Variations of thetype
$$\int_{\Omega}f(x, Du)\ {\rm d}x$$
where Ω is a bounded open set in $\mathbb{R}^{n}$ , u∈ $W^{1,p}_{\rm loc}$ (Ω; $\mathbb{R}^{N}$ ), 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 givea bound on the Hausdorff dimension of the singular set of minimizers.