{"title":"薄障碍问题的自由边界部分正则性","authors":"Federico Franceschini, Joaquim Serra","doi":"10.1002/cpa.22152","DOIUrl":null,"url":null,"abstract":"<p>For the thin obstacle problem in <math>\n <semantics>\n <msup>\n <mi>R</mi>\n <mi>n</mi>\n </msup>\n <annotation>$\\mathbb {R}^n$</annotation>\n </semantics></math>, <math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>≥</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$n\\ge 2$</annotation>\n </semantics></math>, we prove that at <i>all</i> free boundary points, with the exception of a <math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>n</mi>\n <mo>−</mo>\n <mn>3</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$(n-3)$</annotation>\n </semantics></math>-dimensional set, the solution differs from its blow-up by higher order corrections. This expansion entails a <i>C</i><sup>1, 1</sup>-type free boundary regularity result, up to a codimension 3 set.</p>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Free boundary partial regularity in the thin obstacle problem\",\"authors\":\"Federico Franceschini, Joaquim Serra\",\"doi\":\"10.1002/cpa.22152\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For the thin obstacle problem in <math>\\n <semantics>\\n <msup>\\n <mi>R</mi>\\n <mi>n</mi>\\n </msup>\\n <annotation>$\\\\mathbb {R}^n$</annotation>\\n </semantics></math>, <math>\\n <semantics>\\n <mrow>\\n <mi>n</mi>\\n <mo>≥</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$n\\\\ge 2$</annotation>\\n </semantics></math>, we prove that at <i>all</i> free boundary points, with the exception of a <math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>n</mi>\\n <mo>−</mo>\\n <mn>3</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$(n-3)$</annotation>\\n </semantics></math>-dimensional set, the solution differs from its blow-up by higher order corrections. This expansion entails a <i>C</i><sup>1, 1</sup>-type free boundary regularity result, up to a codimension 3 set.</p>\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2023-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22152\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22152","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Free boundary partial regularity in the thin obstacle problem
For the thin obstacle problem in , , we prove that at all free boundary points, with the exception of a -dimensional set, the solution differs from its blow-up by higher order corrections. This expansion entails a C1, 1-type free boundary regularity result, up to a codimension 3 set.
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