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Remarks about Hardy inequalities on metric trees

Ekholm, Tomas and Frank, Rupert L. and Kovařík, Hynek (2007) Remarks about Hardy inequalities on metric trees. . (Submitted)

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We find sharp conditions on the growth of a rooted regular metric tree such that the Neumann Laplacian on the tree satisfies a Hardy inequality. In particular, we consider homogeneous metric trees. Moreover, we show that a non-trivial Aharonov-Bohm magnetic field leads to a Hardy inequality on a loop graph.

Item Type:Report or Paper (Discussion Paper)
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Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. (Submitted on 13 Nov 2007) The authors are grateful to Timo Weidl for several useful discussions, and to the organizers of the workshop ‘Analysis on Graphs’ at the Isaac Newton Institute in Cambridge for their kind invitation. This work has been supported by FCT grant SFRH/BPD/23820/2005 (T.E.) and DAAD grant D/06/49117 (R.F.). Partial support by the ESF programme SPECT (T.E. and H.K.) and the DAAD-STINT PPP programme (R.F.) is gratefully acknowledged.
Funding AgencyGrant Number
Fundação para a Ciência e a Tecnologia (FCT)SFRH/BPD/23820/2005
Deutscher Akademischer Austauschdienst (DAAD)D/06/49117
European Science FoundationUNSPECIFIED
Swedish Foundation for International Cooperation in Research and Higher Education (STINT)UNSPECIFIED
Subject Keywords:Laplace operator, metric tree, Hardy inequality
Record Number:CaltechAUTHORS:20170512-090412324
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77393
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:46
Last Modified:09 Mar 2020 13:18

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