A refined estimate for the topological degree

Hoai-Minh Nguyen

doi:10.1016/j.crma.2017.10.007

Mathematical analysis/Differential topology

A refined estimate for the topological degree
[Une estimée raffinée du degré topologique]

Présenté par : Haïm Brézis

Hoai-Minh Nguyen ¹

¹ École polytechnique fédérale de Lausanne, EPFL, SB MATHAA CAMA, Station 8, CH-1015 Lausanne, Switzerland

Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1046-1049.

Résumé
Abstract

Nous affinons une estimée du degré topologique pour des applications continues d'une sphère $S^{d}$ dans elle-même dans le cas $d \geq 2$ . Cela fournit la réponse pour $d \geq 2$ à une question posée par Brezis. Le problème est encore ouvert pour $d = 1$ .

We sharpen an estimate of [4] for the topological degree of continuous maps from a sphere $S^{d}$ into itself in the case $d \geq 2$ . This provides the answer for $d \geq 2$ to a question raised by Brezis. The problem is still open for $d = 1$ .

Reçu le : 2017-10-08
Accepté le : 2017-10-12
Publié le : 2017-10-01

DOI : 10.1016/j.crma.2017.10.007

Affiliations des auteurs :

Hoai-Minh Nguyen ¹

¹ École polytechnique fédérale de Lausanne, EPFL, SB MATHAA CAMA, Station 8, CH-1015 Lausanne, Switzerland

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     author = {Hoai-Minh Nguyen},
     title = {A refined estimate for the topological degree},
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     language = {en},
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Hoai-Minh Nguyen. A refined estimate for the topological degree. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1046-1049. doi : 10.1016/j.crma.2017.10.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.007/

Bibliographie
Cité par

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[2] J. Bourgain; H. Brezis; P. Mironescu Lifting, degree, and distributional Jacobian revisited, Commun. Pure Appl. Math., Volume 58 (2005), pp. 529-551

[3] J. Bourgain; H. Brezis; P. Mironescu Complements to the paper “Lifting, Degree, and Distributional Jacobian Revisited” | HAL

[4] J. Bourgain; H. Brezis; H-M. Nguyen A new estimate for the topological degree, C. R. Acad. Sci. Paris, Ser. I, Volume 340 (2005), pp. 787-791

[5] J. Bourgain; H-M. Nguyen A new characterization of Sobolev spaces, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 75-80

[6] H. Brezis (Prog. Math.), Volume vol. 244, Birkhäuser (2006), pp. 137-154

[7] H. Brezis, Private communication, 2006.

[8] H-M. Nguyen Some new characterizations of Sobolev spaces, J. Funct. Anal., Volume 237 (2006), pp. 689-720

[9] H-M. Nguyen Optimal constant in a new estimate for the degree, J. Anal. Math., Volume 101 (2007), pp. 367-395

[10] H-M. Nguyen Some inequalities related to Sobolev norms, Calc. Var. Partial Differ. Equ., Volume 41 (2011), pp. 483-509

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