Semilinear subelliptic problems without compactness on Lie groups

Ian Schindler (1) , Cyril Tintarev (2)

1 MIP - Mathématiques pour l'Industrie et la Physique
2 Department of Mathematics [Uppsala]

An abstract version of concentration compactness on Hilbert spaces applies to the actions of non-compact Lie groups. Using the concentration-compactness argument we prove the existence of solutions for semilinear problems involving sub-Laplacians on the whole Lie group and on certain of their non-compact subsets, including minimizers for Sobolev inequalities. The result is stated for any real connected finite-dimensional Lie group

Domaines: Equations aux dérivées partielles [math.AP]

Ian Schindler, Cyril Tintarev. Semilinear subelliptic problems without compactness on Lie groups. NoDEA Nonlinear Differential Equations Appl., 2004, 11 (3), pp.299-309. ⟨hal-00982446⟩