Degenerate operators of Tricomi type in \(L^p\)-spaces and in spaces of continuous functions (Q652473)

The authors study elliptic operators \(L\) with Dirichlet boundary conditions over a bounded domain \(\Omega\) whose diffusion coefficients degenerate linearly on \(\partial \Omega \) in tangential directions. The domain of \(L\) is computed and existence, uniqueness and (maximal) regularity of the elliptic and parabolic problems for \(L\) in \(L^p\)-spaces and in spaces of continuous functions are established. Moreover, it is proved that the analytic semigroups generated by \(L\) are consistent, positive, compact and exponentially stable.