Comptes Rendus
no. 9
Functional analysis
Perimeter of sets and BMO-type norms
[Périmètre d'ensembles et normes de type BMO]

Présenté par : Haïm Brezis

Luigi Ambrosio1 ; Jean Bourgain2 ; Haïm Brezis3, 4 ; Alessio Figalli5
1 Scuola Normale Superiore, Piazza Cavalieri 7, 56100 Pisa, Italy
2 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA
3 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA
4 Technion, Department of Mathematics, Haifa 32000, Israel
5 University of Texas at Austin, Mathematics Dept., 2515 Speedway Stop C1200, Austin, TX 78712-1202, USA
Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 697-698.

Dans cette note, nous annonçons des résultats récents montrant qu'une variante isotrope de la norme de type BMO introduite dans [3] peut être reliée par une formule exacte au périmètre d'ensembles.

The aim of this note is to announce some recent results showing that an isotropic variant of the BMO-type norm introduced in [3] can be related via a precise formula to the perimeter of sets.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.07.001

Luigi Ambrosio 1 ; Jean Bourgain 2 ; Haïm Brezis 3, 4 ; Alessio Figalli 5

1 Scuola Normale Superiore, Piazza Cavalieri 7, 56100 Pisa, Italy
2 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA
3 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA
4 Technion, Department of Mathematics, Haifa 32000, Israel
5 University of Texas at Austin, Mathematics Dept., 2515 Speedway Stop C1200, Austin, TX 78712-1202, USA 
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     title = {Perimeter of sets and {\protect\emph{BMO}-type} norms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {697--698},
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Luigi Ambrosio; Jean Bourgain; Haïm Brezis; Alessio Figalli. Perimeter of sets and BMO-type norms. Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 697-698. doi : 10.1016/j.crma.2014.07.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.07.001/

[1] L. Ambrosio, H. Brezis, J. Bourgain, A. Figalli, BMO-type norms related to the perimeter of sets. Preprint, 2014.

[2] F. Barthe; B. Maurey Some remarks on isoperimetry of Gaussian type, Ann. Inst. Henri Poincaré B, Probab. Stat., Volume 36 (2000), pp. 419-434

[3] J. Bourgain, H. Brezis, P. Mironescu, A new function space and applications. Preprint, 2014.

[4] H. Hadwiger Gitterperiodische Punktmengen und Isoperimetrie, Monatsh. Math., Volume 76 (1972), pp. 410-418

[5] F. John; L. Nirenberg On functions of bounded mean oscillation, Comm. Pure Appl. Math., Volume 14 (1961), pp. 415-426

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