{"title":"The exterior Dirichlet problem for the homogeneous complex k-Hessian equation","authors":"Zhenghuan Gao, Xinan Ma, Dekai Zhang","doi":"10.1515/ans-2022-0039","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ⧹ Ω {{\\mathbb{C}}}^{n}\\setminus \\Omega . We prove the existence and uniqueness of the C 1 , 1 {C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2022-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Nonlinear Studies","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ans-2022-0039","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: 2
Abstract
Abstract In this article, we consider the homogeneous complex k k -Hessian equation in an exterior domain C n ⧹ Ω {{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C 1 , 1 {C}^{1,1} solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second-order estimate.
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.
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