Given a group of symmetries on a (generally non-compact) differentiable manifold, we construct invariant locally subelliptic operators, prove Sobolev inequalities and verify existence of correspondent minimizers. The results apply, in particular, to a class of singular elliptic operators on domains in R
N with singularity on the boundary.
Keywords subelliptic operators - Sobolev inequalities - homogeneous spaces - Lie groups - symmetric spaces - weak convergence - concentration compactness - sub-Riemannian geometry
Mathematics Subject Classifications (2000) 35H20, 35J20, 40A30, 22E30, 43A85.
K. Tintarev: Research supported by a grant from Vetenskaprådet.