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Etude asymptotique et multiplicité pour l'équation de Sobolev Poincaré

Abstract : On a compact Riemannian manifold of dimension larger than 3,
we consider a particular elliptic non linear equation : the Sobolev Poincaré equation. Firstly, we describe the asymptotic behaviour of sequences of solutions of this equation thanks to a fine analysis of the concentration phenomenon. Then we get results of multiplicity of solutions for this equation by introducing isometry invariances. Our method gives also multiplicity results for more classical critical equations like the Yamabe or the Nirenberg equation, and also for overcritical equations. Our work is strongly related to the description of the best constants in functionnal inequalities of Sobolev.
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https://tel.archives-ouvertes.fr/tel-00261595
Contributor : Marie Dellinger <>
Submitted on : Friday, March 7, 2008 - 3:57:07 PM
Last modification on : Wednesday, December 9, 2020 - 3:09:35 PM
Long-term archiving on: : Thursday, May 20, 2010 - 8:08:18 PM

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  • HAL Id : tel-00261595, version 1

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Marie Dellinger. Etude asymptotique et multiplicité pour l'équation de Sobolev Poincaré. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2007. Français. ⟨tel-00261595⟩

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