Comptes Rendus
no. 11
Mathematical Analysis
A new estimate for the topological degree

Presented by: Haïm Brezis

Jean Bourgain1; Haïm Brezis2, 3; Hoai-Minh Nguyen2
1 Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA
2 Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 175, rue du Chevaleret, 75013 Paris, France
3 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA
Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 787-791.

We establish a new estimate for the topological degree of continuous maps from the sphere SN into itself, which answers a question raised in Bourgain, Brezis, and Mironescu [Commun. Pure Appl. Math. 58 (2005) 529–551] and extends some of the results proved there, as well as in recent work by these authors (Lifting, degree, and distributional Jacobian revisited, http://ann.jussieu.fr/publications).

Nous présentons une nouvelle estimée du degré topologique pour des applications continues de la sphère SN dans elle-même. Celle-ci répond à une question posée dans Bourgain, Brezis, et Mironescu [Commun. Pure Appl. Math. 58 (2005) 529–551] et généralise certains résultats de cet article ainsi que du travail récent de ces auteurs (Lifting, degree, and distributional Jacobian revisited, http://ann.jussieu.fr/publications).

Received:
Published online:
DOI: 10.1016/j.crma.2005.04.007

Jean Bourgain 1; Haïm Brezis 2, 3; Hoai-Minh Nguyen 2

1 Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA
2 Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 175, rue du Chevaleret, 75013 Paris, France
3 Rutgers University, Department of Mathematics, Hill Center, Busch Campus, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA 
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Jean Bourgain; Haïm Brezis; Hoai-Minh Nguyen. A new estimate for the topological degree. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 787-791. doi : 10.1016/j.crma.2005.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.04.007/

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

[2] J. Bourgain; H. Brezis; P. Mironescu Complements to the paper: “Lifting, degree, and distributional Jacobian revisited” http://ann.jussieu.fr/publications (to be posted on the website)

[3] H.-M. Nguyen, Optimal constant in a new estimate for the degree, submitted for publication

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