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A regularity result for a convex functional and bounds for the singularset
Published online by Cambridge University Press: 11 August 2009
Abstract
In this paper we prove a regularity result for local minimizers of functionals of the Calculus of Variations of the type
$$
\int_{\Omega}f(x, Du)\ {\rm d}x
$$
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 give
a bound on the Hausdorff dimension of the singular set of minimizers.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 1002 - 1017
- Copyright
- © EDP Sciences, SMAI, 2009
References
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