A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

被引：49

作者：

Hebey, Emmanuel ^{[1
]}

Pacard, Frank ^{[2
]}

Pollack, Daniel ^{[3
]}

机构：

[1] Univ Cergy Pontoise, Dept Math, F-95302 Cergy Pontoise, France

[2] Univ Paris 12, Dept Math, F-94010 Creteil, France

[3] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 278卷 / 01期

关键词：

D O I：

10.1007/s00220-007-0377-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian constraint equation, which has been previously studied by other methods.

引用

页码：117 / 132

页数：16

共 20 条

[1] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[2] AUBIN T, 1982, GRUND MATH WISSENSCH, V252
[3] Bartnik R, 2004, EINSTEIN EQUATIONS AND THE LARGE SCALE BEHAVIOR OF GRAVITATIONAL FIELDS - 50 YEARS OF THE CAUCHY PROBLEM IN GENERAL RELATIVITY, P1
[4] Brendle S, 2008, J AM MATH SOC, V21, P951
[5] The Einstein-scalar field constraints on asymptotically euclidean manifolds
Choquet-Bruhat, Y
Isenberg, J
Pollack, D
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2006, 27 (01) : 31 - 52
[6] Choquet-Bruhat Y., 1980, General relativity and gravitation. One hundred years after the birth of Albert Einstein, vol.1, P99
[7] The constraint equations for the Einstein-scalar field system on compact manifolds
Choquet-Bruhat, Yvonne
Isenberg, James
Pollack, Daniel
[J]. CLASSICAL AND QUANTUM GRAVITY, 2007, 24 (04) : 809 - 828
[8] GLOBAL ASPECTS OF CAUCHY PROBLEM IN GENERAL RELATIVITY
CHOQUETBRUHAT, Y
GEROCH, R
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1969, 14 (04) : 329 - +
[9] Blow-up examples for second order elliptic PDEs of critical Sobolev growth
Druet, O
Hebey, E
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (05) : 1915 - 1929
[10] *THEOREME DEXISTENCE POUR CERTAINS SYSTEMES DEQUATIONS AUX DERIVEES PARTIELLES NON LINEAIRES
FOURESBRUHAT, Y
[J]. ACTA MATHEMATICA, 1952, 88 (03) : 141 - 225

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