عنوان

An Analysis of the Conformal Formulation of the Einstein Constraint Equations on Asymptotically FlatManifolds

Number

TL47m8t3wn

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

An Analysis of the Conformal Formulation of the Einstein Constraint Equations on Asymptotically FlatManifolds

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[Thesis]

First Statement of Responsibility

Behzadan, Ali

Name of Publisher, Distributor, etc.

UC San Diego

Date of Publication, Distribution, etc.

2015

Body granting the degree

UC San Diego

Text preceding or following the note

2015

Text of Note

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

Behzadan, Ali

UC San Diego

Electronic name

p

[Thesis]

276903

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Y