Generators with interior degeneracy on spaces of L^2 type

Abstract

We consider operators in divergence and in nondivergence form with degeneracy at the interior of the space domain. Characterizing the domain of the operators, we prove that they generate positive analytic semigroups on spaces of L^2 type. Finally, some applications to linear and semilinear parabolic evolution problems and to linear hyperbolic ones are presented.

Keywords

• Degenerate operators in divergence and non divergence form
• linear and semiliner parabolic equations
• linear hyperbolic equations