A regularity result for a convex functional and bounds for the singular set
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1002-1017.

In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the type

Ω f(x,Du)dx
where Ω is a bounded open set in n , u W loc 1,p (Ω; 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 give a bound on the Hausdorff dimension of the singular set of minimizers.

DOI : 10.1051/cocv/2009030
Classification : 35J50, 35J60, 35B65
Mots clés : partial regularity, singular sets, fractional differentiability, variational integrals
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De Maria, Bruno. A regularity result for a convex functional and bounds for the singular set. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1002-1017. doi : 10.1051/cocv/2009030. http://archive.numdam.org/articles/10.1051/cocv/2009030/

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