| Issue |
ESAIM: COCV
Volume 16, Number 4, October-December 2010
|
|
|---|---|---|
| Page(s) | 1002 - 1017 | |
| DOI | https://doi.org/10.1051/cocv/2009030 | |
| Published online | 11 August 2009 | |
A regularity result for a convex functional and bounds for the singular set
Dipartimento di Matematica e Applicazioni “R. Caccioppoli” Università
di Napoli “Federico II” Via Cintia, 80126 Napoli, Italy. bruno.demaria@dma.unina.it
Received:
4
February
2009
Revised:
6
May
2009
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.
Mathematics Subject Classification: 35J50 / 35J60 / 35B65
Key words: Partial regularity / singular sets / fractional differentiability / variational integrals
© EDP Sciences, SMAI, 2009
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