{"title":"具有给定边界值的 $m$ 次谐函数加权能级中的复杂 $m$-Hessian 型方程","authors":"Nguyen Van Phu, Nguyen Quang Dieu","doi":"arxiv-2408.07528","DOIUrl":null,"url":null,"abstract":"In this paper, we concern with the existence of solutions of the complex\n$m-$Hessian type equation $-\\chi(u)H_{m}(u)=\\mu$ in the class\n$\\mathcal{E}_{m,\\chi}(f,\\Omega)$ if there exists subsolution in this class,\nwhere the given boundary value $f\\in\\mathcal{N}_m(\\Omega)\\cap MSH_m(\\Omega).$","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value\",\"authors\":\"Nguyen Van Phu, Nguyen Quang Dieu\",\"doi\":\"arxiv-2408.07528\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we concern with the existence of solutions of the complex\\n$m-$Hessian type equation $-\\\\chi(u)H_{m}(u)=\\\\mu$ in the class\\n$\\\\mathcal{E}_{m,\\\\chi}(f,\\\\Omega)$ if there exists subsolution in this class,\\nwhere the given boundary value $f\\\\in\\\\mathcal{N}_m(\\\\Omega)\\\\cap MSH_m(\\\\Omega).$\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"14 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-14\",\"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-2408.07528\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.07528","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Complex $m$-Hessian type equations in weighted energy classes of $m$-subharmonic functions with given boundary value
In this paper, we concern with the existence of solutions of the complex
$m-$Hessian type equation $-\chi(u)H_{m}(u)=\mu$ in the class
$\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class,
where the given boundary value $f\in\mathcal{N}_m(\Omega)\cap MSH_m(\Omega).$
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