{"title":"带角域中具有不连续系数的发散形式椭圆方程","authors":"Jun Chen, Xuemei Deng","doi":"10.1007/s10473-024-0515-2","DOIUrl":null,"url":null,"abstract":"<p>We study equations in divergence form with piecewise <i>C</i><sup><i>α</i></sup> coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise <i>C</i><sup>1,<i>α</i></sup> estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Elliptic equations in divergence form with discontinuous coefficients in domains with corners\",\"authors\":\"Jun Chen, Xuemei Deng\",\"doi\":\"10.1007/s10473-024-0515-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study equations in divergence form with piecewise <i>C</i><sup><i>α</i></sup> coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise <i>C</i><sup>1,<i>α</i></sup> estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.</p>\",\"PeriodicalId\":50998,\"journal\":{\"name\":\"Acta Mathematica Scientia\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Scientia\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10473-024-0515-2\",\"RegionNum\":4,\"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":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0515-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Elliptic equations in divergence form with discontinuous coefficients in domains with corners
We study equations in divergence form with piecewise Cα coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise C1,α estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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