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.

Detalles Bibliográficos
Autor principal: Usman, Muhammad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182407/
https://www.ncbi.nlm.nih.gov/pubmed/30363811
http://dx.doi.org/10.1186/s13660-018-1872-y
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author Usman, Muhammad
author_facet Usman, Muhammad
author_sort Usman, Muhammad
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description 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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spelling pubmed-61824072018-10-22 Sobolev type inequalities for compact metric graphs Usman, Muhammad J Inequal Appl Research 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. Springer International Publishing 2018-10-05 2018 /pmc/articles/PMC6182407/ /pubmed/30363811 http://dx.doi.org/10.1186/s13660-018-1872-y Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Usman, Muhammad
Sobolev type inequalities for compact metric graphs
title Sobolev type inequalities for compact metric graphs
title_full Sobolev type inequalities for compact metric graphs
title_fullStr Sobolev type inequalities for compact metric graphs
title_full_unstemmed Sobolev type inequalities for compact metric graphs
title_short Sobolev type inequalities for compact metric graphs
title_sort sobolev type inequalities for compact metric graphs
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6182407/
https://www.ncbi.nlm.nih.gov/pubmed/30363811
http://dx.doi.org/10.1186/s13660-018-1872-y
work_keys_str_mv AT usmanmuhammad sobolevtypeinequalitiesforcompactmetricgraphs

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