椭圆型微分算子正确限制的奇异数比较

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2014-11-04 DOI:10.1090/S0077-1554-2014-00229-6

V. Burenkov, M. Otelbaev

{"title":"椭圆型微分算子正确限制的奇异数比较","authors":"V. Burenkov, M. Otelbaev","doi":"10.1090/S0077-1554-2014-00229-6","DOIUrl":null,"url":null,"abstract":"The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in Rn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k 2l/n as k → ∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. §","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"863 1","pages":"115-131"},"PeriodicalIF":0.0000,"publicationDate":"2014-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00229-6","citationCount":"0","resultStr":"{\"title\":\"Comparison of the singular numbers of correct restrictions of elliptic differential operators\",\"authors\":\"V. Burenkov, M. Otelbaev\",\"doi\":\"10.1090/S0077-1554-2014-00229-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in Rn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k 2l/n as k → ∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. §\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\"863 1\",\"pages\":\"115-131\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-11-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00229-6\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/S0077-1554-2014-00229-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/S0077-1554-2014-00229-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

研究了定义在边界充分光滑的Rn有界域上的2l阶一致椭圆微分算子的一个正确约束的奇异渐近性，该算子一般为非自伴随算子。建立了一个正确的约束条件，保证其奇异数sk在k→∞时为k 2l/n阶。作为这一结果的一个应用，得到了这类正确约束的奇异数在域摄动时的偏差的某些估计。§

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Comparison of the singular numbers of correct restrictions of elliptic differential operators

The paper is dedicated to finding the asymptotics of singular numbers of a correct restriction of a uniformly elliptic differential operator of order 2l defined on a bounded domain in Rn with sufficiently smooth boundary, which is in general a nonselfadjoint operator. Conditions are established on a correct restriction, ensuring that its singular numbers sk are of order k 2l/n as k → ∞. As an application of this result certain estimates are obtained for the deviation upon domain perturbation of singular numbers of such correct restrictions. §

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

自引率

0.00%

发文量

期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.