紧度量图的Sobolev型不等式。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-10-05 DOI:10.1186/s13660-018-1872-y

Muhammad Usman

引用次数: 0

摘要

本文导出了紧连通度量图的Sobolev不等式的类似形式。作为这些不等式的结果，恢复了具有标准顶点条件的拉普拉斯算子的第一个非零特征值的下界，通常称为Cheeger不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sobolev type inequalities for compact metric graphs.

In this paper analogues of Sobolev inequalities for compact and connected metric graphs are derived. As a consequence of these inequalities, a lower bound, commonly known as Cheeger inequality, on the first non-zero eigenvalue of the Laplace operator with standard vertex conditions is recovered.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.