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Pełne teksty:
Warianty tytułu
Abstrakty
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
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
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 35Q75: PDEs in connection with relativity and gravitational theory
- 35J65: Nonlinear boundary value problems for linear elliptic equations
- 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
- 83C05: Einstein's equations (general structure, canonical formalism, Cauchy problems)
- 35J60: Nonlinear elliptic equations
- 58J32: Boundary value problems on manifolds
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
355
Liczba stron
100
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLV
Daty
wydano
1996
otrzymano
1994-12-19
poprawiono
1995-06-05
Twórcy
autor
- Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden
autor
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, skr. poczt. 137, 00-950 Warszawa, Poland
- Département de Mathématiques, Université de Tours, Parc de Grandmont, 37200 Tours, France
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Języki publikacji
| EN |
Uwagi
1991 Mathematics Subject Classification: Primary 83C05, 35Q75, 53C21; Secondary 58G20, 35J60, 35J65.
Identyfikator YADDA
bwmeta1.element.zamlynska-45ca71a5-8d97-4728-bf7a-a1425f9d95ed
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ISSN
0012-3862
Kolekcja
DML-PL
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