On some infinite sums of integer valued Dirac's masses
[Sur certaines sommes infinies de masses de Dirac entières]
Smets, Didier1
1 Laboratoire d'analyse numerique, Université Pierre et Marie Curie, boite Courrier 187, 75252 Paris cedex 05, France
Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 371-374.

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.

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.

Reçu le :
Publié le :
DOI : 10.1016/S1631-073X(02)02270-7
Smets, Didier 1

1 Laboratoire d'analyse numerique, Université Pierre et Marie Curie, boite Courrier 187, 75252 Paris cedex 05, France 
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Smets, Didier. On some infinite sums of integer valued Dirac's masses. Comptes Rendus. Mathématique, Tome 334 (2002) no. 5, pp. 371-374. doi : 10.1016/S1631-073X(02)02270-7. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02270-7/

[1] Ambrosio, L.; Kirchheim, B. Currents in metric spaces, Acta Math., Volume 185 (2000) no. 1, pp. 1-80

[2] Bourgain, J.; Brezis, H.; Mironescu, P. On the structure of the Sobolev space H1/2 with values into the circle, C. R. Acad. Sci. Paris, Sér. I, Volume 331 (2000) no. 2, pp. 119-124

[3] Brezis, H.; Coron, J.-M.; Lieb, E. Harmonic maps with defects, Comm. Math. Phys., Volume 7 (1986), pp. 649-705

[4] Federer, H. Geometric Measure Theory, Springer-Verlag, Berlin, 1969

[5] Jerrard, R.L.; Soner, H.M. Rectifiability of the distributional Jacobian for a class of functions, C. R. Acad. Sci. Paris, Sér. I, Volume 329 (1999) no. 8, pp. 683-688

[6] R.L. Jerrard, H.M. Soner, Functions of bounded higher variation, Preprint, 1999

[7] Rivière, T. Dense subsets of H1/2(S2,S1), Ann. Global Anal. Geom., Volume 18 (2000) no. 5, pp. 517-528

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