Analisi Matematica

Research topics

Regularity of operators with anisotropic and general growth
Marcellini, Mascolo, Vespri
Semicontinuity in the Calculus of Variations
Marcellini, Mascolo, De Pascale, Focardi
Fractional Operators
Vespri
Density functional theory for Coulomb or interacting systems
De Pascale
Optimal transport problems and applications
De Pascale
Variational solutions to evolutionary problems
Marcellini, De Pascale
Free discontinuity problems
Focardi
Free boundary problems
Focardi, Geraci

Non-autonomous dynamical systems and ergodic theory
Fabbri
PDE’s and infinite dimensional dynamical systems: long-time behavior, attractors
Bisconti, Bucci

Optimal Control, Hamiltonian methods, Geometric control
Poggiolini, Sarychev, Spadini
Control of Partial Differential Equations (PDE’s) and Infinite Dimensional Systems
Bucci, Sarychev
Nonautonomous linear control systems
Fabbri

Applications to mathematical physics
Bisconti, Gianni, Magnanini, Salani
Geometric and functional inequalities
Bianchini, Cianchi, Gronchi, Magnanini, Salani
Qualitative properties of solutions
Bianchini, Cianchi, Colesanti, Francini, Magnanini, Salani, Vespri
Quantitative estimates of unique continuation
Francini, Vessella
Regularity estimates
Bisconti, Bucci, Gianni, Vespri

Qualitative theory for ordinary differential equations and inclusions
Anichini, Bisconti, Conti, Matucci, Spadini, Villari, Zecca
Boundary value problems on compact and noncompact intervals
Anichini, Conti, Matucci, Pera, Villari, Zecca
Functional differential and differential-difference equations and inclusions
Matucci, Pera, Villari, Zecca
Topological methods for ordinary differential equations and inclusions
Anichini, Bisconti, Conti, Matucci, Pera, Spadini, Villari, Zecca,
Non-autonomous dynamics: non-autonomous dynamical systems and ergodic theory
Fabbri, Johnson
Topological dynamics: Lypaunov exponents, exponential dychotomies and rotation numbers
Fabbri, Johnson
Non autonomous Hamiltonian systems, quasi-periodic Schroedinger operators
Fabbri, Johnson
Bifurcation theory
Fabbri, Johnson