{"title":"Triebel-Lizorkin尺度下准共形映射的全局平滑性","authors":"Kari Astala , Martí Prats , Eero Saksman","doi":"10.1016/j.matpur.2024.04.008","DOIUrl":null,"url":null,"abstract":"<div><p>We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000412/pdfft?md5=f62675a2e198d50e0c28eb49218cd39b&pid=1-s2.0-S0021782424000412-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale\",\"authors\":\"Kari Astala , Martí Prats , Eero Saksman\",\"doi\":\"10.1016/j.matpur.2024.04.008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000412/pdfft?md5=f62675a2e198d50e0c28eb49218cd39b&pid=1-s2.0-S0021782424000412-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000412\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000412","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
We study quasiconformal mappings in planar domains Ω and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to optimal conditions, in terms of the geometry of the boundary ∂Ω and of the smoothness of the Beltrami coefficient, that guarantee the global regularity of the mappings in these classes. In the Triebel-Lizorkin class with smoothness below 1, the same conditions give global regularity in Ω for the principal solutions with Beltrami coefficient supported in Ω.
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