Abstract: In this talk we intend to present higher order regularity results for weak solutions to quasilinear subelliptic equations in a non-nilpotent case. More precisely, we use the vector fields generating the Lie Algebra of the special orthogonal group SO(3). Until now similar results have been obtained in the case of vector fields generating the Lie algebra of nilpotent stratified Lie groups. In a non-nilpotent case a new approach is necessary, because for all the previous higher order regularity results for nonlinear quasilinear subellptic PDEs the existence of a center for the Lie Algebra constituted a key factor.
This is a joint work with Juan J. Manfredi.