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Theses

Phénomène de concentration pour des
problèmes non linéaires issus de la géométrie

Abstract : In this Thesis, we study concentration phenomena for geometrical nonlinear elliptic equations : the existence of constant r-curvature hypersurfaces in Riemannian manifolds. ( The r-mean curvature of a hypersurfave is defined to be the r-th elementary symmetric function of the principal curvature of the hypersurface). We give in this thesis some results of existence of such a submanifolds. Moreover, the
examples we build highlight a concentration phenomena along submanifolds, phenomena associated with a resonance phenomena which returns the analysis of these objects particularly delicate and which one meets in the study of many other nonlinear problems : nonlinear Schrödinger equations, singularly perturbed problems, reaction-diffusion systems, ...
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Submitted on : Monday, February 27, 2006 - 6:44:24 PM
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Fethi Mahmoudi. Phénomène de concentration pour des
problèmes non linéaires issus de la géométrie. Mathématiques [math]. Université Paris XII Val de Marne, 2005. Français. ⟨tel-00011695⟩

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