Remarks about Hardy inequalities on metric trees

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.

References in corpus (1)

• Schrödinger operator on homogeneous metric trees: spectrum in gaps

Cited by in corpus (1)

• NLS ground states on metric trees: existence results and open questions