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Theses

Inegalites de Gagliardo-Nirenberg optimales sur les varietes riemanniennes

Abstract : Sobolev spaces are inherent to the theory of PDEs. The embedding theorems of these spaces into the Lebesgue spaces gives the Sobolev inequalities. S. L. Sobolev introduced these notions in the 30s and they are now a fundamental tool in analysis. Some other mathematicians developed this topic.One may cite E. Gagliardo and L. Nirenberg in the 50s. The study of optimal Sobolev inequalities began with great problems in analysis such as the Yamabe problem. There exist different approaches. We are interested in two of them: the AB program and the BA program. The first one was studied by T. Aubin, O. Druet, E. Hebey and M. Vaugon. D. Bakry and M. Ledoux studied the second one in Markov semi-group theory. Sobolev inequalities are a sub-family of Gagliardo-Nirenberg inequalities. So it is natural to ask if an extension of the previous works is possible. First, a positive answer was given for Nash and Sobolev logarithmic inequalities. In this thesis, we adapt the AB program and the BA program to a larger sub-family of Gagliardo-Nirenberg inequalities including the Nash inequality.
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Contributor : Christophe Brouttelande <>
Submitted on : Sunday, March 21, 2004 - 6:46:36 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
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Christophe Brouttelande. Inegalites de Gagliardo-Nirenberg optimales sur les varietes riemanniennes. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2003. Français. ⟨tel-00005408⟩

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