An Analysis of the Conformal Formulation of the Einstein Constraint Equations on Asymptotically Flat...

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" An Analysis of the Conformal Formulation of the Einstein Constraint Equations on Asymptotically FlatManifolds "
Behzadan, Ali

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	905752
Doc. No	:	TL47m8t3wn
Main Entry	:	Behzadan, Ali
Title & Author	:	An Analysis of the Conformal Formulation of the Einstein Constraint Equations on Asymptotically FlatManifolds\ Behzadan, Ali
College	:	UC San Diego
Date	:	2015
student score	:	2015
Abstract	:	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
Added Entry	:	UC San Diego