{"title":"Regularity of degenerate k-Hessian equations on closed Hermitian manifolds","authors":"Dekai Zhang","doi":"10.1515/ans-2022-0025","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we are concerned with the existence of weak C 1 , 1 {C}^{1,1} solution of the k k -Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation. The key points are to show the weak C 1 , 1 {C}^{1,1} estimates. We prove a Cherrier-type inequality to obtain the C 0 {C}^{0} estimate, and the complex Hessian estimate is proved by using an auxiliary function, which was motivated by Hou et al. and Tosatti and Weinkove. Our result generalizes the Kähler case proved by Dinew et al.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":"22 1","pages":"534 - 547"},"PeriodicalIF":2.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Nonlinear Studies","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ans-2022-0025","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this article, we are concerned with the existence of weak C 1 , 1 {C}^{1,1} solution of the k k -Hessian equation on a closed Hermitian manifold under the optimal assumption of the function in the right-hand side of the equation. The key points are to show the weak C 1 , 1 {C}^{1,1} estimates. We prove a Cherrier-type inequality to obtain the C 0 {C}^{0} estimate, and the complex Hessian estimate is proved by using an auxiliary function, which was motivated by Hou et al. and Tosatti and Weinkove. Our result generalizes the Kähler case proved by Dinew et al.
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.