Conference Paper

A Short Note on the Classical Hardy Inequality and Its Applications to Sobolev Spaces

The Hardy inequality is among the most influential inequalities in mathematical analysis, with significant applications in functional analysis, partial differential equations, Sobolev spaces, and numerical methods. This paper presents a concise overview of the classical Hardy inequality, outlines its foundational proof, discusses its intrinsic relationship with Sobolev spaces, and highlights selected applications in computational mathematics. A weighted extension of the inequality and a simple illustrative example are also presented to demonstrate its practical validity. Keywords: Hardy inequality; Sobolev spaces; partial differential equations; weighted inequalities; numerical analysis.