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Solutions of the constraint equations in general relativity satisfying "hyperboloidal boundary conditions"

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Andersson L., Chruściel P. T.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 1. Introduction .............................................................................................5 2. The hyperboloidal initial value problem....................................................9 2.1. Conformal compactifications and Cauchy data....................................9 2.2. Some remarks on non-vacuum initial data sets..................................14 3. Definitions, preliminary results................................................................16 3.1. Function spaces.................................................................................16 3.2. Some embeddings..............................................................................22 3.3. Extensions of functions defined on ∂M...............................................24 3.4. Mapping properties of some integral operators..................................26 4. Regularity at the boundary: the linear problem......................................30 4.1. Tangential regularity below the threshold...........................................30 4.2. Boundary regularity for a class of second order systems...................39 5. Non-linear equations with polyhomogeneous coefficients......................52 5.1. Polyhomogeneity of solutions of some fully non-linear equations.......52 6. The vector constraint equation...............................................................57 6.1. Introductory remarks..........................................................................57 6.2. (Non-weighted) Hölder spaces on the compactified manifold.............58 6.3. Weighted Sobolev spaces..................................................................66 7. The Lichnerowicz equation.....................................................................74 7.1. Introductory remarks..........................................................................74 7.2. The linearized equation.....................................................................76 7.3. Existence of solutions of the non-linear problem................................79 7.4. Regularity at the boundary of the solutions........................................81 Appendix A. Genericity of log-terms...........................................................87 A.1. The vector constraint equation..........................................................88 A.2. The coupled system...........................................................................91 Appendix B.................................................................................................94 B.1. "Almost Gaussian" coordinates..........................................................94 References................................................................................................96 Index of symbols........................................................................................99 Index of terms..........................................................................................100

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1 Andersson L.

1 Chruściel P. T.

1 1996

Wyniki wyszukiwania

Solutions of the constraint equations in general relativity satisfying "hyperboloidal boundary conditions"