KTH/SU Mathematics Colloquium
October 15, 2008
Adimurthi
Critical exponent problem in two dimensions
Critical exponent problems are non-compact problems which arise in studying
many geometrical phenomena. In view of the Trudinger Imbedding, the critical exponent in
two dimensions vastly differs from that in higher dimensions. For example, the best constants
are always achieved by the results of Moser, Carleson and Chang. This is in contrast
with that in higher dimensions. In this talk I will describe the existence, uniqueness and
blow-up phenomena for the critical exponent problem in two dimensions.