Geometric methods in free boundaries problems
Research focus
The Peer review has evaluated this group as Excellent
The main research topics are: I) Regularity in free boundary problems. The focus is on: optimal regularity of solutions of obstacle problems for subelliptic operators (J10); study of the regularity of viscosity solutions and their free boundaries for stationary and evolution problems (B1, J2); problems involving the curvature of the free boundary (J1, J12). II) Segregation in competing species systems and optimal partition problems. The focus is: analysis of the stationary states for reaction-diffusion systems of many densities having disjoint supports (J6, J7, J9); study of the asymptotic behavior of a class of population models as the competition rate tends to infinity (J5, J8) III) Variational methods for ODE’s. Study of sub and superlinear ODE forced oscillators (J4, J11, J13). IV) Uniqueness questions for viscosity solutions. The focus is on positive uniqueness results for viscosity solutions of parabolic equation with discontinuous coefficients (J3) (a quite delicate problem).
Dipartimento di afferenza
Docenti afferenti
Full Professors
Sandro Salsa
Associate Professors
Maria Cristina Cerutti
Assistant Professors
Gianmaria Verzini