Interior W2,p estimate for small perturbations to the complex Monge–AmpÈre equation

Jingrui Cheng; Yulun Xu

doi:10.1007/s00526-023-02571-x

Interior W²^,^p estimate for small perturbations to the complex Monge–AmpÈre equation

Jingrui Cheng
, Yulun Xu

Mathematics

Stony Brook University

Stony Brook University

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

3 Scopus citations

Abstract

Let w be a bounded, C³ , strictly plurisubharmonic function defined on B₁⊂ Cⁿ . Then w has a neighborhood in L^∞(B₁) with the following property: for any continuous, plurisubharmonic function u in this neighborhood solving 1 - ε≤ MA(u) ≤ 1 + ε , one has u∈W2,p(B12) , as long as ε> 0 is small enough depending only on n and p. This partially generalizes Caffarelli’s interior W²^,^p estimates for real Monge–Ampère to the complex version.

Original language	English
Article number	231
Journal	Calculus of Variations and Partial Differential Equations
Volume	62
Issue number	8
DOIs	https://doi.org/10.1007/s00526-023-02571-x
State	Published - Nov 2023

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title = "Interior W2,p estimate for small perturbations to the complex Monge–Amp{\`E}re equation",

abstract = "Let w be a bounded, C3 , strictly plurisubharmonic function defined on B1⊂ Cn . Then w has a neighborhood in L∞(B1) with the following property: for any continuous, plurisubharmonic function u in this neighborhood solving 1 - ε≤ MA(u) ≤ 1 + ε , one has u∈W2,p(B12) , as long as ε> 0 is small enough depending only on n and p. This partially generalizes Caffarelli{\textquoteright}s interior W2,p estimates for real Monge–Amp{\`e}re to the complex version.",

author = "Jingrui Cheng and Yulun Xu",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s00526-023-02571-x",

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T1 - Interior W2,p estimate for small perturbations to the complex Monge–AmpÈre equation

AU - Cheng, Jingrui

AU - Xu, Yulun

PY - 2023/11

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N2 - Let w be a bounded, C3 , strictly plurisubharmonic function defined on B1⊂ Cn . Then w has a neighborhood in L∞(B1) with the following property: for any continuous, plurisubharmonic function u in this neighborhood solving 1 - ε≤ MA(u) ≤ 1 + ε , one has u∈W2,p(B12) , as long as ε> 0 is small enough depending only on n and p. This partially generalizes Caffarelli’s interior W2,p estimates for real Monge–Ampère to the complex version.

AB - Let w be a bounded, C3 , strictly plurisubharmonic function defined on B1⊂ Cn . Then w has a neighborhood in L∞(B1) with the following property: for any continuous, plurisubharmonic function u in this neighborhood solving 1 - ε≤ MA(u) ≤ 1 + ε , one has u∈W2,p(B12) , as long as ε> 0 is small enough depending only on n and p. This partially generalizes Caffarelli’s interior W2,p estimates for real Monge–Ampère to the complex version.

UR - https://www.scopus.com/pages/publications/85172008105

U2 - 10.1007/s00526-023-02571-x

DO - 10.1007/s00526-023-02571-x

M3 - Article

SN - 0944-2669

VL - 62

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 8

M1 - 231

ER -

Interior W²^,^p estimate for small perturbations to the complex Monge–AmpÈre equation

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