Properties of linear and nonlinear elliptic operators

Research themes:

• Mean value property for the Laplacian and sub-Laplacians;
• Existence and regularity of solutions for systems of partial differential equations and functionals of the calculus of variations;
• Regularity properties of free boundaries in two-phase problems for linear and nonlinear elliptic and parabolic operators;
• Properties of nonlocal elliptic and subelliptic operators of fractional type;
• Regularity of viscosity solutions for quasilinear operators;
• Geometric properties of solutions of nonlinear operators associated with the Hessian matrix or bi-Laplacian operators;
• Structure results of radial solutions of critical and supercritical problems with nonautonomous dynamical systems techniques;
• Stability analysis of the solutions to parabolic problems with reaction terms of power type.

External Collaborators:

Bruno Franchi, Paolo Marcellini, Elvira Mascolo, Sandro Salsa, Daniela De Silva, Qing Liu, Juan Manfredi, Ireneo Peral, Ermanno Lanconelli, Luca Capogna, Isabella Birindelli, Italo Capuzzo Dolcetta, Claudia Lederman, Serena Dipierro, Antonio Vitolo, Andrea Pinamonti, Andrea Sfecci, Michal Pospisil, Giorgio Tortone, Alberto Boscaggin, Benedetto Noris.