Concentration compactness and nonlinear subelliptic problems without compactness

Kyril Tintarev Uppsala University, Sweden

An abstract version of concentration compactness on Hilbert spaces applies to to actions of Lie groups. Using the concentration-compactness argument we prove existence of solutions for semilinear problems involving sub-Laplacians on whole Lie groups and on their certain non-compact subsets. The main assumption on the group and the sub-Laplacian is compactness of Folland-Stein embedding in the local case. This is a joint work with Ian Schindler