Symmetry breaking results for problems with exponential growth in the unit disk

We investigate some asymptotic properties of extrema uα to the two- dimensional variational problem sup u∈H1 0(B) k uk =1 Z B � e γu 2 1 � |x| α dx as � ! +1. Here B is the unit disk of R 2 and 0 < � 4� is a given parameter. We prove that in a certain range of 's, the maximizers are not radial forlarge.