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" Atlas optischer Erscheinungen / Atlas de phénomènes d'optique / Atlas of optical phenomena "
von Michel Cagnet, Maurice Françon, Jean Claude Thrierr.
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Latin Dissertation
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English
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905752
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TL47m8t3wn
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| Main Entry
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Behzadan, Ali
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An Analysis of the Conformal Formulation of the Einstein Constraint Equations on Asymptotically FlatManifolds\ Behzadan, Ali
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UC San Diego
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2015
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2015
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| Abstract
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In this thesis we consider the conformal formulation of the Einstein constraintequations on asymptotically flat (AF) manifolds. The conformal method transforms the original underdetermined system of constraint equations into a potentially well-posed nonlinear elliptic system which is referred to as Lichnerowicz-Choquet-Bruhat-York (LCBY) system. We investigate the important properties of weighted Sobolev spaces as the appropriate solution spaces for the LCBY equations on AF manifolds. We combine elliptic estimates, sub- and supersolution constructions, fixed-point theorems, and Fredholm-Riesz-Schauder theory to establish existence of non-CMC weak solutions of the LCBY equations for AF manifolds of class Ŵ{s,p}_{\delta} where p\in (1,\infty), s \in (1+3/p ,\infty), -1<\delta<0, with metric in the positive Yamabe class
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UC San Diego
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