Logarithmic Refinements of a Power Weighted Hardy--Rellich-Type Inequality

TL;DR

This paper establishes a logarithmic refinement of the power weighted Hardy--Rellich inequality applicable to all dimensions greater than or equal to two, broadening the scope of existing inequalities in mathematical analysis.

Contribution

It introduces a new logarithmic refinement of the Hardy--Rellich inequality valid for all parameters and dimensions, extending previous results in the field.

Findings

Proves a logarithmic refinement of the Hardy--Rellich inequality

Applicable to all dimensions n ≥ 2

Valid for the broadest range of parameters

Abstract

The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on $n$-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions $n \in \mathbb{N}$, $n\geq 2$.