{"title":"平面多边形域上Monge-AmpeÉre方程的全局C2，α估计","authors":"N. Le, O. Savin","doi":"10.1353/ajm.2023.0004","DOIUrl":null,"url":null,"abstract":"Abstract:We classify global solutions of the Monge-Amp\\\\`ere equation $\\\\det D^2 u=1$ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^\\{2,\\\\alpha\\}$ estimates for the non-degenerate Monge-Amp\\\\`ere equation in convex polygonal domains in $\\\\Bbb\\{R\\}^2$ provided a globally $C^2$, convex strict subsolution exists.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Global C2,α estimates for the Monge-Ampère equation on polygonal domains in the plane\",\"authors\":\"N. Le, O. Savin\",\"doi\":\"10.1353/ajm.2023.0004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract:We classify global solutions of the Monge-Amp\\\\\\\\`ere equation $\\\\\\\\det D^2 u=1$ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^\\\\{2,\\\\\\\\alpha\\\\}$ estimates for the non-degenerate Monge-Amp\\\\\\\\`ere equation in convex polygonal domains in $\\\\\\\\Bbb\\\\{R\\\\}^2$ provided a globally $C^2$, convex strict subsolution exists.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1353/ajm.2023.0004\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1353/ajm.2023.0004","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Global C2,α estimates for the Monge-Ampère equation on polygonal domains in the plane
Abstract:We classify global solutions of the Monge-Amp\\`ere equation $\\det D^2 u=1$ on the first quadrant in the plane with quadratic boundary data. As an application, we obtain global $C^\{2,\\alpha\}$ estimates for the non-degenerate Monge-Amp\\`ere equation in convex polygonal domains in $\\Bbb\{R\}^2$ provided a globally $C^2$, convex strict subsolution exists.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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