Comptes Rendus
Calculus of Variations
Non-differentiable functionals and singular sets of minima
Comptes Rendus. Mathématique, Volume 340 (2005) no. 1, pp. 93-98.

We provide bounds for the Hausdorff dimension of the singular set of minima of functionals of the type ΩF(x,v,Dv), where F is only Hölder continuous with respect to the variables (x,v).

Nous bornons la dimension de Hausdorff de l'ensemble singulier des minima de fonctionnelles du type ΩF(x,v,Dv)F n'est Hölderienne que par rapport aux la variables (x,v).

Published online:
DOI: 10.1016/j.crma.2004.11.019

Jan Kristensen 1; Giuseppe Mingione 2

1 Mathematical Institute, University of Oxford, St. Giles' 24-29, Oxford OX1 3LB, UK
2 Dipartimento di Matematica, Università di Parma, via D'Azeglio 85/a, 43100, Parma, Italy
     author = {Jan Kristensen and Giuseppe Mingione},
     title = {Non-differentiable functionals and singular sets of minima},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2005},
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Jan Kristensen; Giuseppe Mingione. Non-differentiable functionals and singular sets of minima. Comptes Rendus. Mathématique, Volume 340 (2005) no. 1, pp. 93-98. doi : 10.1016/j.crma.2004.11.019.

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