Some new estimates for the complex Monge-Ampère equation

Xiuxiong Chen; Jingrui Cheng

doi:10.1007/s11425-019-1600-8

Some new estimates for the complex Monge-Ampère equation

Mathematics

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3 Scopus citations

Abstract

In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get L^p (p < ∞) and L^∞ estimates for the gradient of the solution in terms of the continuity of the right-hand side.

Original language	English
Pages (from-to)	2073-2088
Number of pages	16
Journal	Science China Mathematics
Volume	62
Issue number	11
DOIs	https://doi.org/10.1007/s11425-019-1600-8
State	Published - Nov 1 2019

Keywords

32W20
35R01
complex Monge-Ampère equations
gradient estimates
Kähler manifold

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10.1007/s11425-019-1600-8

Cite this

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title = "Some new estimates for the complex Monge-Amp{\`e}re equation",

abstract = "In this paper, we consider the complex Monge-Amp{\`e}re equation posed on a compact Kahler manifold. We show how to get Lp (p < ∞) and L∞ estimates for the gradient of the solution in terms of the continuity of the right-hand side.",

keywords = "32W20, 35R01, complex Monge-Amp{\`e}re equations, gradient estimates, K{\"a}hler manifold",

author = "Xiuxiong Chen and Jingrui Cheng",

note = "Publisher Copyright: {\textcopyright} 2019, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Cheng, Jingrui

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N2 - In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get Lp (p < ∞) and L∞ estimates for the gradient of the solution in terms of the continuity of the right-hand side.

AB - In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get Lp (p < ∞) and L∞ estimates for the gradient of the solution in terms of the continuity of the right-hand side.

KW - 32W20

KW - 35R01

KW - complex Monge-Ampère equations

KW - gradient estimates

KW - Kähler manifold

UR - https://www.scopus.com/pages/publications/85074715347

U2 - 10.1007/s11425-019-1600-8

DO - 10.1007/s11425-019-1600-8

M3 - Article

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SN - 1674-7283

VL - 62

SP - 2073

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JO - Science China Mathematics

JF - Science China Mathematics

IS - 11

ER -

Some new estimates for the complex Monge-Ampère equation

Abstract

Keywords

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