Existence of solutions and regularity near the characteristic boundary for sub-Laplacian equations on Carnot groups (Q996145)

The author deals with the problems of existence and regularity of solutions to a nonlinear Dirichlet problem involving sub-Laplacians on Carnot groups. He proves that the best constant in the Folland-Stein embedding theorem on Carnot groups is achieved, which in turn implies the existence of a positive solutions of the Yamabe-type equation on Carnot groups.