$W^{1,p}$ approximation of the Moser--Trudinger inequality

TL;DR

This paper introduces a power-type approximation to the Moser--Trudinger functional and demonstrates that its concentration level approaches the Carleson--Chang limit, providing new insights into functional analysis and inequalities.

Contribution

It presents a novel power approximation method for the Moser--Trudinger inequality and establishes convergence of the concentration level to a known limit.

Findings

Convergence of the approximation to the Carleson--Chang limit

New method for approximating the Moser--Trudinger functional

Insights into concentration phenomena in functional inequalities

Abstract

We propose a power type approximation of the Moser--Trudinger functional and show that its concentration level converges to the Carleson--Chang limit.