A regularity result for a convex functional and bounds for the singular set
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, p. 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 : https://doi.org/10.1051/cocv/2009030
Classification:  35J50,  35J60,  35B65
Keywords: partial regularity, singular sets, fractional differentiability, variational integrals
@article{COCV_2010__16_4_1002_0,
     author = {De Maria, Bruno},
     title = {A regularity result for a convex functional and bounds for the singular set},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     pages = {1002-1017},
     doi = {10.1051/cocv/2009030},
     zbl = {1203.35088},
     mrnumber = {2744159},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2010__16_4_1002_0}
}
De Maria, Bruno. A regularity result for a convex functional and bounds for the singular set. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, pp. 1002-1017. doi : 10.1051/cocv/2009030. http://www.numdam.org/item/COCV_2010__16_4_1002_0/

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