C2α-estimate for Monge-Ampère equations with Hölder-continuous right hand side

Xiuxiong Chen; Yuanqi Wang

doi:10.1007/s10455-015-9487-8

C²α-estimate for Monge-Ampère equations with Hölder-continuous right hand side

Xiuxiong Chen
, Yuanqi Wang

Mathematics

University of California at Santa Barbara

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

18 Scopus citations

Abstract

We present a somewhat new proof to the (Formula presented.) a priori estimate for the uniform elliptic Monge-Ampère equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the (Formula presented.) -norm of the right-hand side of the equation.

Original language	English
Pages (from-to)	195-204
Number of pages	10
Journal	Annals of Global Analysis and Geometry
Volume	49
Issue number	2
DOIs	https://doi.org/10.1007/s10455-015-9487-8
State	Published - Mar 1 2016

Keywords

Conic kähler metrics
Monge-Ampère equation
Schauder estimate

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10.1007/s10455-015-9487-8

Cite this

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title = "C2α-estimate for Monge-Amp{\`e}re equations with H{\"o}lder-continuous right hand side",

abstract = "We present a somewhat new proof to the (Formula presented.) a priori estimate for the uniform elliptic Monge-Amp{\`e}re equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the (Formula presented.) -norm of the right-hand side of the equation.",

keywords = "Conic k{\"a}hler metrics, Monge-Amp{\`e}re equation, Schauder estimate",

author = "Xiuxiong Chen and Yuanqi Wang",

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language = "English",

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T1 - C2α-estimate for Monge-Ampère equations with Hölder-continuous right hand side

AU - Chen, Xiuxiong

AU - Wang, Yuanqi

PY - 2016/3/1

Y1 - 2016/3/1

N2 - We present a somewhat new proof to the (Formula presented.) a priori estimate for the uniform elliptic Monge-Ampère equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the (Formula presented.) -norm of the right-hand side of the equation.

AB - We present a somewhat new proof to the (Formula presented.) a priori estimate for the uniform elliptic Monge-Ampère equations, in both the real and complex settings. Our estimates do not need to differentiate the equation, and only depends on the (Formula presented.) -norm of the right-hand side of the equation.

KW - Conic kähler metrics

KW - Monge-Ampère equation

KW - Schauder estimate

UR - https://www.scopus.com/pages/publications/84959209171

U2 - 10.1007/s10455-015-9487-8

DO - 10.1007/s10455-015-9487-8

M3 - Article

AN - SCOPUS:84959209171

SN - 0232-704X

VL - 49

SP - 195

EP - 204

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 2

ER -

C²α-estimate for Monge-Ampère equations with Hölder-continuous right hand side

Abstract

Keywords

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