Global smoothness for a singular Monge–Ampère equation

Huaiyu Jian; Xu Jia Wang; Yuwen Zhao

doi:10.1016/j.jde.2017.08.004

Global smoothness for a singular Monge–Ampère equation

Huaiyu Jian^*, Xu Jia Wang, Yuwen Zhao

^*Corresponding author for this work

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

25 Citations (Scopus)

Abstract

The global C^n+2,α-regularity for the graph of solutions to a singular Monge–Ampère equation was established in [7]. This equation arises in the study of hyperbolic affine spheres and is singular at the boundary. A compatibility condition for higher regularity was found in [7]. In this paper, we verify the compatibility condition and obtain the global C^∞-regularity in the even dimensional case.

Original language	English
Pages (from-to)	7250-7262
Number of pages	13
Journal	Journal of Differential Equations
Volume	263
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2017.08.004
Publication status	Published - 5 Dec 2017

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title = "Global smoothness for a singular Monge–Amp{\`e}re equation",

abstract = "The global Cn+2,α-regularity for the graph of solutions to a singular Monge–Amp{\`e}re equation was established in [7]. This equation arises in the study of hyperbolic affine spheres and is singular at the boundary. A compatibility condition for higher regularity was found in [7]. In this paper, we verify the compatibility condition and obtain the global C∞-regularity in the even dimensional case.",

author = "Huaiyu Jian and Wang, {Xu Jia} and Yuwen Zhao",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

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T1 - Global smoothness for a singular Monge–Ampère equation

AU - Jian, Huaiyu

AU - Wang, Xu Jia

AU - Zhao, Yuwen

PY - 2017/12/5

Y1 - 2017/12/5

N2 - The global Cn+2,α-regularity for the graph of solutions to a singular Monge–Ampère equation was established in [7]. This equation arises in the study of hyperbolic affine spheres and is singular at the boundary. A compatibility condition for higher regularity was found in [7]. In this paper, we verify the compatibility condition and obtain the global C∞-regularity in the even dimensional case.

AB - The global Cn+2,α-regularity for the graph of solutions to a singular Monge–Ampère equation was established in [7]. This equation arises in the study of hyperbolic affine spheres and is singular at the boundary. A compatibility condition for higher regularity was found in [7]. In this paper, we verify the compatibility condition and obtain the global C∞-regularity in the even dimensional case.

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U2 - 10.1016/j.jde.2017.08.004

DO - 10.1016/j.jde.2017.08.004

M3 - Article

SN - 0022-0396

VL - 263

SP - 7250

EP - 7262

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -

Global smoothness for a singular Monge–Ampère equation

Abstract

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