Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds

Fuente: arXiv
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Main Authors: Ciulică, Cristian, Rugină, Teodor
Format: Preprint
Published: 2025
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author Ciulică, Cristian
Rugină, Teodor
author_facet Ciulică, Cristian
Rugină, Teodor
contents In this paper we prove sharp multipolar Hardy-type inequalities in the Riemannian $L^p-$setting for $p\geq 2$ using the method of super-solutions and fundamental results from comparison theory on manifolds, thus generalizing previous results for $p=2$. We emphasize that when we restrict to Cartan-Hadamard manifolds, the inequalities improve in the case $2<p<N$ compared to the case $p=2$ since we obtain positive remainder terms which are controlled by curvature estimates. In the end, we treat the cases of positive and negative constant sectional curvature.
format Preprint
id arxiv_https___arxiv_org_abs_2503_04703
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds
Ciulică, Cristian
Rugină, Teodor
Analysis of PDEs
35A23, 35B25, 53C21, 58J60
In this paper we prove sharp multipolar Hardy-type inequalities in the Riemannian $L^p-$setting for $p\geq 2$ using the method of super-solutions and fundamental results from comparison theory on manifolds, thus generalizing previous results for $p=2$. We emphasize that when we restrict to Cartan-Hadamard manifolds, the inequalities improve in the case $2<p<N$ compared to the case $p=2$ since we obtain positive remainder terms which are controlled by curvature estimates. In the end, we treat the cases of positive and negative constant sectional curvature.
title Sharp multipolar $L^p$-Hardy-type inequalities on Riemannian manifolds
topic Analysis of PDEs
35A23, 35B25, 53C21, 58J60
url https://arxiv.org/abs/2503.04703