The complex Monge-Ampère equation on compact Kähler manifolds

Xiuxiong Chen; Weiyong He

doi:10.1007/s00208-012-0780-6

The complex Monge-Ampère equation on compact Kähler manifolds

Xiuxiong Chen
, Weiyong He

Mathematics

University of Oregon

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

23 Scopus citations

Abstract

We consider the complex Monge-Ampère equation on a compact Kähler manifold (M, g) when the right hand side F has rather weak regularity. In particular we prove that estimate of Δφ and the gradient estimate hold when F is in W ^1,p0 for any p ₀ > 2n. As an application, we show that there exists a classical solution in W ^3,p0 for the complex Monge-Ampère equation when F is in W ^1,p0.

Original language	English
Pages (from-to)	1583-1600
Number of pages	18
Journal	Mathematische Annalen
Volume	354
Issue number	4
DOIs	https://doi.org/10.1007/s00208-012-0780-6
State	Published - Nov 2012

Access to Document

10.1007/s00208-012-0780-6

Cite this

@article{0c7efbe6f09943bb8f1bb9711ed03951,

title = "The complex Monge-Amp{\`e}re equation on compact K{\"a}hler manifolds",

abstract = "We consider the complex Monge-Amp{\`e}re equation on a compact K{\"a}hler manifold (M, g) when the right hand side F has rather weak regularity. In particular we prove that estimate of Δφ and the gradient estimate hold when F is in W 1,p0 for any p 0 > 2n. As an application, we show that there exists a classical solution in W 3,p0 for the complex Monge-Amp{\`e}re equation when F is in W 1,p0.",

author = "Xiuxiong Chen and Weiyong He",

year = "2012",

month = nov,

doi = "10.1007/s00208-012-0780-6",

language = "English",

volume = "354",

pages = "1583--1600",

journal = "Mathematische Annalen",

issn = "0025-5831",

number = "4",

}

TY - JOUR

T1 - The complex Monge-Ampère equation on compact Kähler manifolds

AU - Chen, Xiuxiong

AU - He, Weiyong

PY - 2012/11

Y1 - 2012/11

N2 - We consider the complex Monge-Ampère equation on a compact Kähler manifold (M, g) when the right hand side F has rather weak regularity. In particular we prove that estimate of Δφ and the gradient estimate hold when F is in W 1,p0 for any p 0 > 2n. As an application, we show that there exists a classical solution in W 3,p0 for the complex Monge-Ampère equation when F is in W 1,p0.

AB - We consider the complex Monge-Ampère equation on a compact Kähler manifold (M, g) when the right hand side F has rather weak regularity. In particular we prove that estimate of Δφ and the gradient estimate hold when F is in W 1,p0 for any p 0 > 2n. As an application, we show that there exists a classical solution in W 3,p0 for the complex Monge-Ampère equation when F is in W 1,p0.

UR - https://www.scopus.com/pages/publications/84869081514

U2 - 10.1007/s00208-012-0780-6

DO - 10.1007/s00208-012-0780-6

M3 - Article

AN - SCOPUS:84869081514

SN - 0025-5831

VL - 354

SP - 1583

EP - 1600

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 4

ER -

The complex Monge-Ampère equation on compact Kähler manifolds

Abstract

Access to Document

Other files and links

Fingerprint

Cite this