Non-differentiable functionals and singular sets of minima

Jan Kristensen; Giuseppe Mingione

doi:10.1016/j.crma.2004.11.019

Calculus of Variations

Non-differentiable functionals and singular sets of minima
[Fonctionnelles non-différentiable et l'ensembles singulier des minima]

Présenté par : John M. Ball

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

Comptes Rendus. Mathématique, Volume 340 (2005) no. 1, pp. 93-98.

Résumé
Abstract

Nous bornons la dimension de Hausdorff de l'ensemble singulier des minima de fonctionnelles du type $\int_{Ω} F (x, v, D v)$ oú F n'est Hölderienne que par rapport aux la variables $(x, v)$ .

We provide bounds for the Hausdorff dimension of the singular set of minima of functionals of the type $\int_{Ω} F (x, v, D v)$ , where F is only Hölder continuous with respect to the variables $(x, v)$ .

Reçu le : 2004-11-02
Accepté le : 2004-11-05
Publié le : 2004-12-21

DOI : 10.1016/j.crma.2004.11.019

Affiliations des auteurs :

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

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     title = {Non-differentiable functionals and singular sets of minima},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {93--98},
     publisher = {Elsevier},
     volume = {340},
     number = {1},
     year = {2005},
     doi = {10.1016/j.crma.2004.11.019},
     language = {en},
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.019/

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