The heat flow with a critical exponential nonlinearity

Tobias Lamm (1) , Frédéric Robert (2) , Michael Struwe (3)

1 UBC Mathematics - Department of Mathematics [Vancouver]
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 D-MATH - Department of Mathematics [ETH Zurich]

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

Domaines: Equations aux dérivées partielles [math.AP]

Tobias Lamm, Frédéric Robert, Michael Struwe. The heat flow with a critical exponential nonlinearity. Journal of Functional Analysis, 2009, 257 (9), pp. 2951-2998. ⟨10.1016/j.jfa.2009.05.018⟩. ⟨hal-01279398⟩