Quantification of Blow-up Levels for a 2-D Elliptic Equation with Critical Exponential Nonlinearity

  • Date: 06/06/2006

Olivier Druet (Ecole Normale Supérieure de Lyon & CNRS)


University of British Columbia


We study sequences of solutions of some elliptic PDE’s, on
2-dimensional bounded domain, with critical Moser-Trudinger exponential
nonlinearity. We prove that lack of compactness occur only when
standard bubbles appear and thus we can quantify the levels of blow-up
of the underlying functional. The main difficulties, compared to the
higher-dimensional situation (Yamabe-type equations), are that
subtracting a bubble to a solution changes the nature of the equation
satisfied by it and that one has to avoid degenerate bubbles, which
could a priori appear as in the study of Chern-Simon vortices.

Other Information: 

DG-MP-PDE Seminar 2006