Dirichlet problem with L^p boundary data for real sub-Laplacians
Ermanno Lanconelli · Le Matematiche · 2005
Let L be a real sub-Laplacian on a stratified Lie group G. In this note we present some results on the Dirichlet problem for L with L^p-boundary data, on domains which are contractible with respect to the natural dilations of G. One of the main difficulties we overcome is the presence of non-regular boundary points for the usual Dirichlet problem for L. A potential theoretical approach is followed.