{"title":"抛物复合 Monge-Ampère 和 Hessian 方程的 $L^\\infty$ 估计值","authors":"Xiuxiong Chen, Jingrui Cheng","doi":"10.4310/pamq.2023.v19.n6.a10","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a version of parabolic complex Monge–Ampère equations, and use a PDE approach similar to Phong <i>et al.</i> to establish $L^\\infty$ and Hölder estimates. We also generalize the $L^\\infty$ estimates to parabolic Hessian equations.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":"64 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The $L^\\\\infty$ estimates for parabolic complex Monge–Ampère and Hessian equations\",\"authors\":\"Xiuxiong Chen, Jingrui Cheng\",\"doi\":\"10.4310/pamq.2023.v19.n6.a10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a version of parabolic complex Monge–Ampère equations, and use a PDE approach similar to Phong <i>et al.</i> to establish $L^\\\\infty$ and Hölder estimates. We also generalize the $L^\\\\infty$ estimates to parabolic Hessian equations.\",\"PeriodicalId\":54526,\"journal\":{\"name\":\"Pure and Applied Mathematics Quarterly\",\"volume\":\"64 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Pure and Applied Mathematics Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2023.v19.n6.a10\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pure and Applied Mathematics Quarterly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2023.v19.n6.a10","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The $L^\infty$ estimates for parabolic complex Monge–Ampère and Hessian equations
In this paper, we consider a version of parabolic complex Monge–Ampère equations, and use a PDE approach similar to Phong et al. to establish $L^\infty$ and Hölder estimates. We also generalize the $L^\infty$ estimates to parabolic Hessian equations.
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