{"title":"论分层集合上谐函数的可移动奇点","authors":"N. S. Dairbekov, O. M. Penkin, D. V. Savasteev","doi":"10.1134/S1064562424601379","DOIUrl":null,"url":null,"abstract":"<p>We consider sets removable for bounded harmonic functions on a stratified set with flat interior strata. It is proved that relatively closed sets of finite Hausdorff <span>\\((n - 2)\\)</span>-measure are removable for bounded harmonic functions on an <i>n</i>-dimensional stratified set satisfying the strong sturdiness condition.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 1","pages":"297 - 300"},"PeriodicalIF":0.5000,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Removable Singularities of Harmonic Functions on a Stratified Set\",\"authors\":\"N. S. Dairbekov, O. M. Penkin, D. V. Savasteev\",\"doi\":\"10.1134/S1064562424601379\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider sets removable for bounded harmonic functions on a stratified set with flat interior strata. It is proved that relatively closed sets of finite Hausdorff <span>\\\\((n - 2)\\\\)</span>-measure are removable for bounded harmonic functions on an <i>n</i>-dimensional stratified set satisfying the strong sturdiness condition.</p>\",\"PeriodicalId\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":\"110 1\",\"pages\":\"297 - 300\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1064562424601379\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424601379","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们考虑在具有平坦内层的分层集合上有界谐函数的可移动集合。证明了有限 Hausdorff \((n-2)\)度量的相对闭集对于满足强坚固性条件的 n 维分层集合上的有界谐函数是可移动的。
On Removable Singularities of Harmonic Functions on a Stratified Set
We consider sets removable for bounded harmonic functions on a stratified set with flat interior strata. It is proved that relatively closed sets of finite Hausdorff \((n - 2)\)-measure are removable for bounded harmonic functions on an n-dimensional stratified set satisfying the strong sturdiness condition.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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