Remarks about Hardy inequalities on metric trees
Spectral Theory
2010-09-24 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0711.1943,
title = {Remarks about Hardy inequalities on metric trees},
author = {Tomas Ekholm and Rupert L. Frank and Hynek Kovarik},
journal= {arXiv preprint arXiv:0711.1943},
year = {2010}
}