On some infinite sums of integer valued Dirac's masses

Didier Smets

doi:10.1016/S1631-073X(02)02270-7

On some infinite sums of integer valued Dirac's masses
[Sur certaines sommes infinies de masses de Dirac entières]

Didier Smets ¹

¹ Laboratoire d'analyse numerique, Université Pierre et Marie Curie, boite Courrier 187, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 371-374.

Abstract (VO)
Résumé

We give a simple proof of a result obtained by Bourgain, Brezis and Mironescu [2] concerning special distributions arising as singular Jacobian determinants. The strong relation of the problem with boundary rectifiability theorems is discussed, and an interesting question remains open.

On donne une démonstration simple d'un résultat obtenu par Bourgain, Brezis et Mironescu [2] concernant certains déterminants jacobiens singuliers. La preuve utilise la relation forte du problème avec les théoremes de rectifiabilité du bord en théorie géometrique de la mesure. Un problème intéressant reste ouvert.

Reçu le : 2001-12-17
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02270-7

Affiliations des auteurs :

Didier Smets ¹

¹ Laboratoire d'analyse numerique, Université Pierre et Marie Curie, boite Courrier 187, 75252 Paris cedex 05, France

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Didier Smets. On some infinite sums of integer valued Dirac's masses. Comptes Rendus. Mathématique, Volume 334 (2002) no. 5, pp. 371-374. doi : 10.1016/S1631-073X(02)02270-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02270-7/

Bibliographie
Cité par

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Luigi Ambrosio; Francesco Ghiraldin Flat chains of finite size in metric spaces, Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, Volume 30 (2013) no. 1, pp. 79-100 | DOI:10.1016/j.anihpc.2012.06.002 | Zbl:1261.49013
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Augusto C. Ponce On the distributions of the form $\sum_{i} (δ_{p_{i}} - δ_{n_{i}})$ , Journal of Functional Analysis, Volume 210 (2004) no. 2, pp. 391-435 | DOI:10.1016/s0022-1236(03)00239-8 | Zbl:1066.46029
Jean Bourgain; Haim Brezis; Petru Mironescu $H^{1 / 2}$ maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation, Publications Mathématiques, Volume 99 (2004), pp. 1-115 | DOI:10.1007/s10240-004-0019-5 | Zbl:1051.49030
Augusto C. Ponce On the distributions of the form $\sum_{i} (δ_{p_{i}} - δ_{n_{i}})$ , Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 336 (2003) no. 7, pp. 571-576 | DOI:10.1016/s1631-073x(03)00133-x | Zbl:1031.46045

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