  The paper studies continutity of Moser nonlinearity in two dimensions with
respect to weak convergence. Unlike the critical nonlinearity in the Sobolev
inequality, which lacks weak continuity at any point, Moser functional fails to
be weakly continuous only in an exceptional case of a concentrating sequence of
functions from the Moser family (up to translations and the remainder vanishing
in Sobolev norm). The argument is based on a structural description of the
defect of weak converegence, analogous to the profile decomposition established
by Solimini for Sobolev inequalities, but involving gauge operators specific
for the two-dimensional case.
