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.
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.
Accepted:
Published online:
Luigi Ambrosio 1; Jean Bourgain 2; Haïm Brezis 3, 4; Alessio Figalli 5
@article{CRMATH_2014__352_9_697_0, author = {Luigi Ambrosio and Jean Bourgain and Ha{\"\i}m Brezis and Alessio Figalli}, title = {Perimeter of sets and {\protect\emph{BMO}-type} norms}, journal = {Comptes Rendus. Math\'ematique}, pages = {697--698}, publisher = {Elsevier}, volume = {352}, number = {9}, year = {2014}, doi = {10.1016/j.crma.2014.07.001}, language = {en}, }
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] 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] Gitterperiodische Punktmengen und Isoperimetrie, Monatsh. Math., Volume 76 (1972), pp. 410-418
[5] On functions of bounded mean oscillation, Comm. Pure Appl. Math., Volume 14 (1961), pp. 415-426
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