An extension of Jörgens–Calabi–Pogorelov theorem to parabolic Monge–Ampère equation

Wei Zhang; Jiguang Bao; Bo Wang

doi:10.1007/s00526-018-1363-5

An extension of Jörgens–Calabi–Pogorelov theorem to parabolic Monge–Ampère equation

Wei Zhang, Jiguang Bao^*, Bo Wang

^*Corresponding author for this work

School of Mathematics and Statistics

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

19 Citations (Scopus)

Abstract

We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension n≥ 3 , the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations.

Original language	English
Article number	90
Journal	Calculus of Variations and Partial Differential Equations
Volume	57
Issue number	3
DOIs	https://doi.org/10.1007/s00526-018-1363-5
Publication status	Published - 1 Jun 2018

Keywords

35B08
35B40
35B53
35K96

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10.1007/s00526-018-1363-5

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title = "An extension of J{\"o}rgens–Calabi–Pogorelov theorem to parabolic Monge–Amp{\`e}re equation",

abstract = "We extend a theorem of J{\"o}rgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Amp{\`e}re equation to parabolic Monge–Amp{\`e}re equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension n≥ 3 , the work of Guti{\'e}rrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Amp{\`e}re equations.",

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AU - Bao, Jiguang

AU - Wang, Bo

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N2 - We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension n≥ 3 , the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations.

AB - We extend a theorem of Jörgens, Calabi and Pogorelov on entire solutions of elliptic Monge–Ampère equation to parabolic Monge–Ampère equation, and obtain delicate asymptotic behavior of solutions at infinity. For the dimension n≥ 3 , the work of Gutiérrez and Huang in Indiana Univ. Math. J. 47, 1459–1480 (1998) is an easy consequence of our result. And along the line of approach in this paper, we can treat other parabolic Monge–Ampère equations.

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JF - Calculus of Variations and Partial Differential Equations

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ER -

An extension of Jörgens–Calabi–Pogorelov theorem to parabolic Monge–Ampère equation

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