Sharp discrete Hardy constants in dimensions three and four and strict upper bounds from dimension nine
Year: 2026
Type: preprint
Abstract: For $N\ge3$, let $C(N)$ be the optimal constant in the nearest-neighbour Hardy inequality on $\mathbb Z^N$ with $u(0)=0$, and set $A_N=(N-2)^2/4$. We prove that the continuum coefficient remains an upper bound, $C(N)\le A_N$, in every dimension, and determine the exact values $C(3)=A_3=1/4$ and $C(4)=A_4=1$. In higher dimensions we show $C(N)
Source: arXiv (Cornell University)
Author: Lizama, Carlos
Institution: Universidad de Santiago de Chile
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204909495