Rellich inequalities via Riccati pairs on model space forms
Analysis of PDEs
2025-08-20 v1
Abstract
We present a simple method for proving Rellich inequalities on Riemannian manifolds with constant, non-positive sectional curvature. The method is built upon simple convexity arguments, integration by parts, and the so-called Riccati pairs, which are based on the solvability of a Riccati-type ordinary differential inequality. These results can be viewed as the higher order counterparts of the recent work by Kaj\'ant\'o, Krist\'aly, Peter, and Zhao, discussing Hardy inequalities using Riccati pairs.
Cite
@article{arxiv.2307.10906,
title = {Rellich inequalities via Riccati pairs on model space forms},
author = {Sándor Kajántó},
journal= {arXiv preprint arXiv:2307.10906},
year = {2025}
}