Degenerate operators of Tricomi type in Lp-spaces and in spaces of continuous functions

We study elliptic operators L with Dirichlet boundary conditions on a bounded domain Ω whose diffusion coefficients degenerate linearly at ∂Ω in tangential directions. We compute the domain of L and establish existence, uniqueness and (maximal) regularity of the elliptic and parabolic problems for L in Lp-spaces and in spaces of continuous functions. Moreover, the analytic semigroups generated by L are consistent, positive, compact and exponentially stable.