Improved Hardy inequality with logarithmic term

TL;DR

This paper introduces a new Hardy inequality featuring a double singular kernel and a logarithmic term, providing improved bounds and applications to eigenvalue estimates for the p-Laplacian in bounded domains.

Contribution

It presents a novel Hardy inequality with a double singular kernel and a logarithmic term, extending previous inequalities and applying them to eigenvalue estimation.

Findings

Established a new Hardy inequality with a logarithmic term

Derived lower bounds for the first eigenvalue of the p-Laplacian

Extended Hardy inequalities to include double singular kernels

Abstract

New Hardy type inequality with double singular kernel and with additional logarithmic term in a ball $B\subset \mathbb{R}^n$ is proved. As an application an estimate from below of the first eigenvalue for Dirichlet problem of p-Laplacian in a bounded domain $\Omega\subset \mathbb{R}^n$ is obtain.