Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università di Napoli “Federico II” Via Cintia, 80126 Napoli, Italy. firstname.lastname@example.org
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the type
where 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.
(Received February 4 2009)
(Revised May 6 2009)
(Online publication August 11 2009)
Mathematics Subject Classification: