Existence of the Riemannian exponential application of diffeomorphisms equipped with a Sobolev metric

Nadji Hermas; Smail Djebali

doi:10.1016/j.matpur.2009.11.004

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Existence of the Riemannian exponential application of diffeomorphisms equipped with a Sobolev metric

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Existence of the Riemannian exponential application of diffeomorphisms equipped with a Sobolev metric

Nadji Hermas and Smail Djebali

Journal de mathématiques pures et appliquées, Vol.94(4), pp.433-446

01/10/2010

DOI: https://doi.org/10.1016/j.matpur.2009.11.004

Abstract

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

We prove the existence of geodesics of the weak Riemannian Lie group (Diff H-infinity(R-n), g(Hk)) = (Diff (R-n) boolean AND (Id + boolean AND(k is an element of N) H-k (R-n; R-n)), g(Hk)), where g(Hk) is the weak Sobolev metric of order k. Next, we study the Riemannian exponential mapping induced by this metric. For k = I, the result immediately gives the local existence of solution in C-infinity( :H-infinity(R-n:R-n)) of the n-dimensional analog of the Camassa-Holm's equation on the Euclidean space R-n. (C) 2009 Elsevier Masson SAS.

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Title: Existence of the Riemannian exponential application of diffeomorphisms equipped with a Sobolev metric
Creators - without role: Nadji Hermas - University of Ouargla
Smail Djebali - Laboratoire de Mathématiques d'Orsay
Publication Details: Journal de mathématiques pures et appliquées, Vol.94(4), pp.433-446
Publisher: Elsevier
Number of pages: 14
Identifiers: 9916228808331
Academic Unit: Imam Mohammad Ibn Saud Islamic University (IMSIU)
Language: French
Resource Type: Journal article