A new estimate for the topological degree
نویسندگان
چکیده
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). To cite this article: J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved. Résumé Une nouvelle estimée du degré topologique. 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). Pour citer cet article : J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005). 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved. Version française abrégée Notre résultat principal est l’estimée (2), valable pour toute fonction continue g :S → S , et tout 0 < δ <√2, où C = C(δ,N) est une constante indépendante de g. Elle répond à une question posée dans [1] et généralise l’inégalité suivante prouvée dans [1], pour tout p >N , |degg| C(p,N) ∫
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