Geometric Analysis in Phase-Space and PDEs

Research activities of the group:

• Analytic hypoellipticity of sums of squares of vector fields;
• Local and global solvability of degenerale operators and operators with multiple characteristics;
• Almost-positivity a priori estimates (Fefferman-Phong, Melin, Hörmander) for pseudodifferential and systems of pseudodifferential operators on Rn and on Lie groups;
• Cauchy problem for weakly hyperbolic operators in presence of transitions of the geometry of bicharacteristics;
• Well-posedness of the Cauchy problem for operators with real characteristics;
• Well-posedness of first-order Hamilton-Jacobi equations and propagation of singularities along generalized characteristics;

• Well-posedness, smoothing properties and Strichartz estimates for dispersive equation.

External Collaborators:

Piermarco Cannarsa, Michael Reissig, Wei-Xi Li, Antonio Bove, Gerardo Mendoza, Gigliola Staffilani, Carlo Sinestrari, Michael Ruzhansky, Sandro Coriasco, Karel Pravda-Starov.