The heat flow with a critical exponential nonlinearity

2009/02/25 by Tobias Lamm, Frédéric Robert, Frederic Robert +5
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.0902.4409

final version, to appear in J. Funct. Anal

openalex publication_date 2009/02/25 · arxiv created 2009/05/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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