Remarks about Hardy inequalities on metric trees

Details Remarks about Hardy inequalities on metric trees Remarks about Hardy inequalities on metric trees

2007-11-13

arxiv.org/abs/0711.1943v1

Mathematics

Spectral Theory

Scientific paper

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.

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