Comptes Rendus
no. 7
Partial Differential Equations
Calderón–Zygmund estimates for measure data problems
[Estimations de type Calderon–Zygmund pour des problèmes avec données mesures]

Présenté par : Alain Bensoussan

Giuseppe Mingione1
1 Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/a, Campus, 43100 Parma, Italy
Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 437-442.

On établit de nouveaux résultats d'existence et régularité pour des problèmes elliptiques non-linéaires avec données mesures. Le gradient de la solution appartient lui-même à un espace de Sobolev (fractionnaire) optimal, ce que l'on peut considérer comme une extension de la théorie de Calderón–Zygmund aux problèmes avec données mesures.

New existence and regularity results are given for non-linear elliptic problems with measure data. The gradient of the solution is itself in an optimal (fractional) Sobolev space: this can be considered an extension of Calderón–Zygmund theory to measure data problems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.02.005
Giuseppe Mingione 1

1 Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/a, Campus, 43100 Parma, Italy 
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Giuseppe Mingione. Calderón–Zygmund estimates for measure data problems. Comptes Rendus. Mathématique, Volume 344 (2007) no. 7, pp. 437-442. doi : 10.1016/j.crma.2007.02.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.02.005/

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