Department of Mathematics, University of Patras, Patras 26110, Greece
Abstract:
In this paper we establish the best constants for a Sobolev inequality and a Sobolev trace inequality on compact Riemannian manifolds with boundary, the functions being invariant under the action of a compact subgroup G of the isometry group I(M,g) and we give applications to some nonlinear PDEs with upper critical Sobolev exponent.