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Fonctions critiques et équations aux dérivées partielles elliptiques sur les variétés riemanniennes compactes

Abstract : This thesis studies a familly of non-linear PDE on a compact riemannian manifold of dimension n?3 of the form . These equations have a variational structure and we seek solutions which minimize the energy among those functions u of W1,2 which satisfy Cf(u)= . Th Aubin prooved that one always have , where cn is a constant that depends only of the dimension, and that if this inequality is strict then there exists a minimizing solution to the equation. I show in my work existence theorems in the limiting case when this inequality is an equality by using a notion of « critical function » introduced by E. Hebey and M. Vaugon, and I proove various results concerning these critical functions.
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https://tel.archives-ouvertes.fr/tel-00007685
Contributor : Stephane Collion <>
Submitted on : Wednesday, December 8, 2004 - 5:52:36 PM
Last modification on : Wednesday, December 9, 2020 - 3:04:57 PM
Long-term archiving on: : Friday, April 2, 2010 - 9:44:28 PM

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  • HAL Id : tel-00007685, version 1

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Stephane Collion. Fonctions critiques et équations aux dérivées partielles elliptiques sur les variétés riemanniennes compactes. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2004. Français. ⟨tel-00007685⟩

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