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Theses

Sur quelques questions de géométrie différentielle liées à la théorie des corps et des fils élastiques

Abstract : The aim of this thesis is to study several questions which arise in the theory of elasticity, by using methods of mathematical analysis and differential geometry. In the one-dimensional case, related to the study of elastic wires, we prove some existence, uniqueness and stability results for a curve in Sobolev spaces. Then, we treat the general case of an immersion of arbitrary dimension and co-dimension of a submanifold in an Euclidean space. We show that the classical existence and uniqueness result for such an immersion can be extended up to the boundary of the submanifold, under a specific, but mild, regularity assumption on this set. Moreover, we show that the mapping constructed in this fashion is locally Lipschitz-continuous with respect to suitable topologies. Finally, we reconsider the study of elastic wires, to obtain some linear and nonlinear Korn inequalities for curves in dimension 3.
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https://tel.archives-ouvertes.fr/tel-00009754
Contributor : Marcela Szopos <>
Submitted on : Wednesday, July 13, 2005 - 4:33:09 PM
Last modification on : Wednesday, February 3, 2021 - 4:30:02 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:06:59 PM

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  • HAL Id : tel-00009754, version 1

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Marcela Szopos. Sur quelques questions de géométrie différentielle liées à la théorie des corps et des fils élastiques. Mathématiques [math]. Université Pierre et Marie Curie - Paris VI, 2005. Français. ⟨tel-00009754⟩

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