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^*

^*Corresponding author for this work

Shanghai University
University of Science and Technology of China

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

5 Scopus citations

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.

Original language	English
Article number	20220039
Journal	Advanced Nonlinear Studies
Volume	23
Issue number	1
DOIs	https://doi.org/10.1515/ans-2022-0039
State	Published - 1 Jan 2023
Externally published	Yes

Keywords

complex k-Hessian equation
exterior Dirichlet problem
gradient estimate
k-subharmonic function

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10.1515/ans-2022-0039

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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",

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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

Abstract

Keywords

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