Mathematical Analysis

The members of the group are Raffaella Cilia, Giuseppa Rita Cirmi, Salvatore D’Asero, Giuseppe Di Fazio, Maria Stella Fanciullo, Francesca Faraci, Umberto Guarnotta, Salvatore Leonardi, Salvatore Angelo Marano, Sunra Mosconi, Ornella Naselli, Maria Alessandra Ragusa, Biagio Ricceri, Andrea Scapellato, Daniele Puglisi, Pietro Zamboni. The members of the group investigate many types of problem of Mathematical Analysis, some of which are existence and regularity of solution of partial differential equations, generalisation of partial differential equations, and also more theoretical questions of Functional Analysis.

Elliptic PDEs: The focus of research is on qualitative and geometric properties of generalized solutions to elliptic PDEs and related boundary value problems. Results are on regularity, existence and well-posedness of boundary value problems. (See also here). Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni.

Variational methods and differential equations: It is systematically studied the existence, the multiplicity  and the regularity (up to the boundary of the domain) of  weak solutions to some classes of  non linear elliptic differential operators. Giuseppa Rita Cirmi, Salvatore D’Asero, Salvatore Angelo Marano, Sunra Mosconi, Maria Alessandra Ragusa, Salvatore Leonardi.
 

Methods from functional analysis and non linear analysis and applications to partial differential equations: the research is focused on problems from functional analysis and nonlinear analysis and their applications to certain partial differential equations arising from physics and optimization. In particular, our studies are devoted to some topics from the geometry of Banach spaces, geometric measure theory, multivalued analysis, minimax theory, PDEs and variational problems. Raffaella Cilia, Francesca Faraci, Daniele Puglisi, Biagio Ricceri.