no. 11
Mathematical Analysis
A new estimate for the topological degree
[Une nouvelle estimée du degré topologique]

Présenté par : Haïm Brezis

Bourgain, Jean1 ; Brezis, Haïm2, 3 ; Nguyen, Hoai-Minh2
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, Tome 340 (2005) no. 11, pp. 787-791.

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).

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).

Reçu le :
Publié le :
DOI : 10.1016/j.crma.2005.04.007
Bourgain, Jean 1 ; Brezis, Haïm 2, 3 ; Nguyen, Hoai-Minh 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 
@article{CRMATH_2005__340_11_787_0,
     author = {Bourgain, Jean and Brezis, Ha{\"\i}m and Nguyen, Hoai-Minh},
     title = {A new estimate for the topological degree},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {787--791},
     publisher = {Elsevier},
     volume = {340},
     number = {11},
     year = {2005},
     doi = {10.1016/j.crma.2005.04.007},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2005.04.007/}
}
TY  - JOUR
AU  - Bourgain, Jean
AU  - Brezis, Haïm
AU  - Nguyen, Hoai-Minh
TI  - A new estimate for the topological degree
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 787
EP  - 791
VL  - 340
IS  - 11
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2005.04.007/
DO  - 10.1016/j.crma.2005.04.007
LA  - en
ID  - CRMATH_2005__340_11_787_0
ER  - 
%0 Journal Article
%A Bourgain, Jean
%A Brezis, Haïm
%A Nguyen, Hoai-Minh
%T A new estimate for the topological degree
%J Comptes Rendus. Mathématique
%D 2005
%P 787-791
%V 340
%N 11
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2005.04.007/
%R 10.1016/j.crma.2005.04.007
%G en
%F CRMATH_2005__340_11_787_0
Bourgain, Jean; Brezis, Haïm; Nguyen, Hoai-Minh. A new estimate for the topological degree. Comptes Rendus. Mathématique, Tome 340 (2005) no. 11, pp. 787-791. doi : 10.1016/j.crma.2005.04.007. http://www.numdam.org/articles/10.1016/j.crma.2005.04.007/

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

[2] Bourgain, J.; Brezis, H.; Mironescu, P. 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

Cité par Sources :