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
1Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA
2Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, 175, rue du Chevaleret, 75013 Paris, France
3Rutgers 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

[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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