The L∞ estimates for parabolic complex Monge-Ampère and Hessian equations

Xiuxiong Chen; Jingrui Cheng

doi:10.4310/PAMQ.2023.v19.n6.a10

The L^∞ estimates for parabolic complex Monge-Ampère and Hessian equations

Mathematics

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4 Scopus citations

Abstract

In this paper, we consider a version of parabolic complex Monge-Ampère equations, and use a PDE approach similar to Phong et al. to establish L^∞ and Hölder estimates. We also generalize the L^∞ estimates to parabolic Hessian equations.

Original language	English
Pages (from-to)	2869-2913
Number of pages	45
Journal	Pure and Applied Mathematics Quarterly
Volume	19
Issue number	6
DOIs	https://doi.org/10.4310/PAMQ.2023.v19.n6.a10
State	Published - 2023

Keywords

L estimate
complex Hessian equations
complex Monge-Ampère equations

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10.4310/PAMQ.2023.v19.n6.a10

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title = "The L∞ estimates for parabolic complex Monge-Amp{\`e}re and Hessian equations",

abstract = "In this paper, we consider a version of parabolic complex Monge-Amp{\`e}re equations, and use a PDE approach similar to Phong et al. to establish L∞ and H{\"o}lder estimates. We also generalize the L∞ estimates to parabolic Hessian equations.",

keywords = "L estimate, complex Hessian equations, complex Monge-Amp{\`e}re equations",

author = "Xiuxiong Chen and Jingrui Cheng",

year = "2023",

doi = "10.4310/PAMQ.2023.v19.n6.a10",

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T1 - The L∞ estimates for parabolic complex Monge-Ampère and Hessian equations

AU - Chen, Xiuxiong

AU - Cheng, Jingrui

PY - 2023

Y1 - 2023

N2 - In this paper, we consider a version of parabolic complex Monge-Ampère equations, and use a PDE approach similar to Phong et al. to establish L∞ and Hölder estimates. We also generalize the L∞ estimates to parabolic Hessian equations.

AB - In this paper, we consider a version of parabolic complex Monge-Ampère equations, and use a PDE approach similar to Phong et al. to establish L∞ and Hölder estimates. We also generalize the L∞ estimates to parabolic Hessian equations.

KW - L estimate

KW - complex Hessian equations

KW - complex Monge-Ampère equations

UR - https://www.scopus.com/pages/publications/85184679891

U2 - 10.4310/PAMQ.2023.v19.n6.a10

DO - 10.4310/PAMQ.2023.v19.n6.a10

M3 - Article

AN - SCOPUS:85184679891

SN - 1558-8599

VL - 19

SP - 2869

EP - 2913

JO - Pure and Applied Mathematics Quarterly

JF - Pure and Applied Mathematics Quarterly

IS - 6

ER -

The L^∞ estimates for parabolic complex Monge-Ampère and Hessian equations

Abstract

Keywords

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