A remark on the Hölder regularity of solutions to the complex Hessian equation

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-04-14 DOI:10.1016/j.jfa.2025.111005

Sławomir Kołodziej , Ngoc Cuong Nguyen

引用次数: 0

Abstract

We prove that the Dirichlet problem for the complex Hessian equation has the Hölder continuous solution provided it has a subsolution with this property. Compared to the previous result of Benali-Zeriahi and Charabati-Zeriahi we remove the assumption on the finite total mass of the measure on the right hand side.

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关于复Hessian方程解的Hölder正则性的注释

我们证明，复 Hessian 方程的 Dirichlet 问题只要有一个子解具有这一性质，就有 Hölder 连续解。与贝纳利-泽里亚希和查拉巴蒂-泽里亚希之前的结果相比，我们取消了对右侧度量的有限总质量的假设。

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

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis