Non radial positive solutions for the {H\'enon equation with critical growth

We study the Dirichlet problem in a ball for the Hénon equation with critical growth and we establish, under some conditions, the existence of a positive, non radial solution. The solution is obtained as a minimizer of the quotient functional associated to the problem restricted to appropriate subspaces of H 01 invariant for the action of a subgroup. Analysis of compactness properties of minimizing sequences and careful level estimates are the main ingredients of the proof.