A bipolar Hardy inequality on Finsler manifolds

Ágnes Mester; Alexandru Kristály

doi:10.1109/SACI46893.2019.9111497

paper

A bipolar Hardy inequality on Finsler manifolds

arXiv:2010.06316 · doi:10.1109/SACI46893.2019.9111497

Abstract

We establish a bipolar Hardy inequality on complete, not necessarily reversible Finsler manifolds. We show that our result strongly depends on the geometry of the Finsler structure, namely on the reversibility constant $r_{F}$ and the uniformity constant $l_{F}$ . Our result represents a Finslerian counterpart of the Euclidean multipolar Hardy inequality due to Cazacu and Zuazua (2013) and the Riemannian case considered by Faraci, Farkas and Kristály (2018).