The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

Zhenghuan Gao; Xinan Ma; Dekai Zhang

doi:10.1515/ans-2022-0039

The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

Zhenghuan Gao
, Xinan Ma
, Dekai Zhang^*

^*此作品的通讯作者

Shanghai University
University of Science and Technology of China

科研成果: 期刊稿件 › 文章 › 同行评审

5 引用（Scopus）

摘要

In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ω C. We prove the existence and uniqueness of the C1,1 solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.

源语言	英语
文章编号	20220039
期刊	Advanced Nonlinear Studies
卷	23
期	1
DOI	https://doi.org/10.1515/ans-2022-0039
出版状态	已出版 - 1 1月 2023
已对外发布	是

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@article{23467fc0d8ab470dafa097b81e245d1f,

title = "The exterior Dirichlet problem for the homogeneous complex k-Hessian equation",

abstract = "In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ω C. We prove the existence and uniqueness of the C1,1 solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.",

keywords = "complex k-Hessian equation, exterior Dirichlet problem, gradient estimate, k-subharmonic function",

author = "Zhenghuan Gao and Xinan Ma and Dekai Zhang",

note = "Publisher Copyright: {\textcopyright} 2023 the author(s), published by De Gruyter.",

year = "2023",

month = jan,

day = "1",

doi = "10.1515/ans-2022-0039",

language = "英语",

volume = "23",

journal = "Advanced Nonlinear Studies",

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T1 - The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

AU - Gao, Zhenghuan

AU - Ma, Xinan

AU - Zhang, Dekai

PY - 2023/1/1

Y1 - 2023/1/1

N2 - In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ω C. We prove the existence and uniqueness of the C1,1 solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.

AB - In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ω C. We prove the existence and uniqueness of the C1,1 solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.

KW - complex k-Hessian equation

KW - exterior Dirichlet problem

KW - gradient estimate

KW - k-subharmonic function

UR - https://www.scopus.com/pages/publications/85146176228

U2 - 10.1515/ans-2022-0039

DO - 10.1515/ans-2022-0039

M3 - 文章

AN - SCOPUS:85146176228

SN - 1536-1365

VL - 23

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

IS - 1

M1 - 20220039

ER -

The exterior Dirichlet problem for the homogeneous complex k-Hessian equation

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