The Sharp Log-Sobolev Inequality on a Compact Interval

TL;DR

This paper proves the sharp log-Sobolev inequality specifically for functions defined on a compact interval, establishing precise bounds and conditions for equality.

Contribution

It offers the first rigorous proof of the sharp log-Sobolev inequality on a compact interval, filling a gap in the mathematical literature.

Findings

Established the exact form of the sharp log-Sobolev inequality on a compact interval

Identified conditions under which equality holds

Provided a new proof technique for the inequality

Abstract

We provide a proof of the sharp log-Sobolev inequality on a compact interval.