Published November 13, 2007
| Submitted
Discussion Paper
Open
Remarks about Hardy inequalities on metric trees
- Creators
- Ekholm, Tomas
-
Frank, Rupert L.
- Kovařík, Hynek
Chicago
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Abstract
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.
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.Attached Files
Submitted - 0711.1943.pdf
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Additional details
- Eprint ID
- 77393
- Resolver ID
- CaltechAUTHORS:20170512-090412324
- Fundação para a Ciência e a Tecnologia (FCT)
- SFRH/BPD/23820/2005
- Deutscher Akademischer Austauschdienst (DAAD)
- D/06/49117
- European Science Foundation
- Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
- Created
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2017-05-12Created from EPrint's datestamp field
- Updated
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2020-03-09Created from EPrint's last_modified field