The heat flow with a critical exponential nonlinearity

TL;DR

This paper investigates the behavior of heat flows associated with the Moser-Trudinger energy, establishing quantization results and demonstrating the existence of critical points in supercritical regimes.

Contribution

It introduces new analysis of heat flow concentration phenomena and proves existence results for critical points beyond the subcritical regime.

Findings

Quantization results for heat flows related to Moser-Trudinger energy

Existence of critical points in supercritical regimes

Analogous behavior to elliptic solutions

Abstract

We analyze the possible concentration behavior of heat flows related to the Moser-Trudinger energy and derive quantization results completely analogous to the quantization results for solutions of the corresponding elliptic equation. As an application of our results we obtain the existence of critical points of the Moser-Trudinger energy in a supercritical regime.