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

IF 2.1 2区数学 Q1 MATHEMATICS

Advanced Nonlinear Studies Pub Date : 2022-08-07 DOI:10.1515/ans-2022-0039

Zhenghuan Gao, Xinan Ma, Dekai Zhang

引用次数: 2

Abstract

Abstract In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ⧹ Ω {{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C 1 , 1 {C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.

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齐次复k-Hessian方程的外狄利克雷问题

摘要在本文中，我们考虑了外域Cn⧹Ω中的齐次复k-Hessian方程。通过构造逼近解，证明了C1，1{C}^{1,1}解的存在唯一性。对我们来说，关键是建立一致梯度估计和二阶估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advanced Nonlinear Studies 数学-数学

CiteScore

3.00

自引率

5.60%

发文量

审稿时长

12 months

期刊介绍： Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.