{"title":"全非线性非局部椭圆方程的光滑逼近","authors":"Xavier Fernández-Real","doi":"10.1090/tran/9038","DOIUrl":null,"url":null,"abstract":"We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth (<inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C Superscript normal infinity\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">C^\\infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) solutions.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Smooth approximations for fully nonlinear nonlocal elliptic equations\",\"authors\":\"Xavier Fernández-Real\",\"doi\":\"10.1090/tran/9038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth (<inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper C Superscript normal infinity\\\"> <mml:semantics> <mml:msup> <mml:mi>C</mml:mi> <mml:mi mathvariant=\\\"normal\\\">∞<!-- ∞ --></mml:mi> </mml:msup> <mml:annotation encoding=\\\"application/x-tex\\\">C^\\\\infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) solutions.\",\"PeriodicalId\":23209,\"journal\":{\"name\":\"Transactions of the American Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the American Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tran/9038\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the American Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tran/9038","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are.
This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.
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