Very weak solutions of quadratic Hessian equations

Sławomir Dinew, Szymon Myga
{"title":"Very weak solutions of quadratic Hessian equations","authors":"Sławomir Dinew, Szymon Myga","doi":"arxiv-2409.08852","DOIUrl":null,"url":null,"abstract":"We extend the methods of Lewicka - Pakzad, Sz\\'ekelyhidi - Cao and Li - Qiu\nto study the notion of very weak solutions to the complex $\\sigma_2$ equation\nin domains in $\\mathbb C^n,\\ n\\geq 2$. As a by-product we sharpen the\nregularity threshold of the counterexamples obtained by Li and Qiu in the real\ncase.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08852","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

We extend the methods of Lewicka - Pakzad, Sz\'ekelyhidi - Cao and Li - Qiu to study the notion of very weak solutions to the complex $\sigma_2$ equation in domains in $\mathbb C^n,\ n\geq 2$. As a by-product we sharpen the regularity threshold of the counterexamples obtained by Li and Qiu in the real case.
二次黑森方程的极弱解
我们扩展了 Lewicka - Pakzad, Sz\'ekelyhidi - Cao 和 Li - Qiuto 的方法,研究了复$sigma_2$方程在$mathbb C^n,\ n\geq 2$域中的极弱解的概念。作为副产品,我们提高了李和邱在实例中得到的反例的规律性临界值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信