English

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}
}
R2 v1 2026-06-21T09:42:51.299Z