On the unit disk we study the Moser-Trudinger functional
and its restrictions , where for . We prove that if a sequence of positive critical points of (for some ) blows up as , then , and weakly in and strongly in . Using this fact we also prove that when is large enough, then has no positive critical point, complementing previous existence results by Carleson-Chang, M. Struwe and Lamm-Robert-Struwe.
Cite this article
Andrea Malchiodi, Luca Martinazzi, Critical points of the Moser-Trudinger functional on a disk. J. Eur. Math. Soc. 16 (2014), no. 5, pp. 893–908DOI 10.4171/JEMS/450