Local Solvability of a Class of Degenerate Second Order Operators

This thesis deals with the local solvability problem related to some degenerate second order partial differential operators with smooth and non-smooth coefficients with multiple characteristics. The main class analyzed is the one with smooth coefficients, which generalizes the one introduced by Colombini, Cordaro and Pernazza in [3]. The other classes considered are a variation with non-smooth coefficients of the main class mentioned above. These classes are particularly interesting since, in some cases, the operators are characterized by a changing sign principal symbol, and this changing sign property can negatively affect the local solvability.