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Problèmes inverses pour l'équation de Newton-Einstein pluridimensionnelle

Abstract : We consider the inverse scattering problem and an inverse boundary value problem for the multidimensional Newton-Einstein equation describing the motion of a classical relativistic particle in a static external electromagnetic (or gravitational) field. The nonrelativistic case is also considered. The external field is assumed to be sufficiently regular with sufficient decay at infinity. First we recall (and develop) some results stating the existence and properties of the scattering map. Then we obtain, in particular, the high energies asymptotics of the scattering map, and we show that the external field is uniquely determined (by explicit formulas) from this asymptotics. We finally obtain an uniqueness theorem at fixed energy for the inverse boundary value problem. From this result we deduce, in particular, that at fixed and
sufficiently large energy the scattering map uniquely determines the external field when this one is also assumed to be compactly supported. The results of this Ph. D. Thesis were obtained by developing, in particular, methods of [Gerver-Nadirashvili, 1983] and [R. Novikov, 1999].
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Contributor : Alexandre Jollivet <>
Submitted on : Friday, July 20, 2007 - 5:00:34 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
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  • HAL Id : tel-00164558, version 1



Alexandre Jollivet. Problèmes inverses pour l'équation de Newton-Einstein pluridimensionnelle. Mathématiques [math]. Université de Nantes, 2007. Français. ⟨tel-00164558⟩



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