{"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.
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