Sobolev type inequalities for compact metric graphs

Sobolev type inequalities for compact metric graphs

Abstract 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 recov...

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Bibliographic Details
Main Author: Muhammad Usman
Format: Article
Language:English
Published: SpringerOpen 2018-10-01
Series:Journal of Inequalities and Applications
Subjects:
Sobolev inequalities
Isoperimetric inequalities
Metric graphs
Quantum graphs
Laplace operator
Online Access:http://link.springer.com/article/10.1186/s13660-018-1872-y

Internet

http://link.springer.com/article/10.1186/s13660-018-1872-y

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