Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

Qing Han; Marcus Khuri

doi:10.1080/03605302.2013.837919

Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

Qing Han
, Marcus Khuri

Mathematics

University of Notre Dame
Peking University

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.

Original language	English
Pages (from-to)	2199-2237
Number of pages	39
Journal	Communications in Partial Differential Equations
Volume	38
Issue number	12
DOIs	https://doi.org/10.1080/03605302.2013.837919
State	Published - Dec 2013

Keywords

Blow-up solutions
Generalized Jang equation
Penrose inequality

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10.1080/03605302.2013.837919

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abstract = "The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.",

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AU - Khuri, Marcus

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N2 - The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.

AB - The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up behavior are given, and it is shown that blow-up solutions are not unique.

KW - Blow-up solutions

KW - Generalized Jang equation

KW - Penrose inequality

UR - https://www.scopus.com/pages/publications/84887050131

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DO - 10.1080/03605302.2013.837919

M3 - Article

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SN - 0360-5302

VL - 38

SP - 2199

EP - 2237

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 12

ER -

Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation

Abstract

Keywords

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