Harnack inequality for a class of strongly degenerate elliptic operators formed by Hörmander vector fields (Q634808)

This paper deals with the following strongly degenerate elliptic equation in divergence form \[ -X_j^*(a_{ij}X_iu+d_ju)+b_iX_iu+cu=f-X_i^*h_i. \] The authors prove the local boundedness of solutions and deduce a Harnack-type inequality. These properties enable them to show that the weak solutions to the above equation are continuous with respect to the Carnot-Carathéodory metric.