From Hardy to Rellich inequalities on graphs
Analysis of PDEs
2020-08-26 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schr\"odinger operators afterwards.
Keywords
Cite
@article{arxiv.1909.02286,
title = {From Hardy to Rellich inequalities on graphs},
author = {Matthias Keller and Yehuda Pinchover and Felix Pogorzelski},
journal= {arXiv preprint arXiv:1909.02286},
year = {2020}
}
Comments
20 pages