Analisi Matematica

Research topics

Regularity of operators with anisotropic and general growthMarcellini, Mascolo, Vespri
Semicontinuity in the Calculus of VariationsDe Pascale, Focardi, Marcellini, Mascolo
Fractional OperatorsVespri
Density functional theory for Coulomb or interacting systemsDe Pascale
Optimal transport problems and applicationsDe Pascale
Variational solutions to evolutionary problemsDe Pascale, Lazzaroni, Lucardesi, Marcellini
Free discontinuity problemsFocardi, Lazzaroni
Free boundary problemsFocardi, Geraci
Shape optimization Lucardesi

Theory of convex bodiesBianchi, Bianchini, Colesanti, Gronchi, Longinetti, Lucardesi
Geometric tomographyBianchi, Gronchi, Longinetti
Geometric inequalitiesBianchini, Colesanti, Gronchi, Magnanini, Salani

Non-autonomous dynamical systems and ergodic theoryFabbri
PDE’s and infinite dimensional dynamical systems: long-time behavior, attractorsBisconti, Bucci

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

Applications to mathematical physicsBisconti, Gianni, Lazzaroni, Magnanini, Salani
Geometric and functional inequalitiesBianchini, Cianchi, Gronchi, Lucardesi, Magnanini, Salani
Qualitative properties of solutionsBianchini, Cianchi, Colesanti, Francini, Magnanini, Salani, Vespri
Quantitative estimates of unique continuationFrancini, Vessella
Regularity estimatesBisconti, Bucci, Gianni, Vespri

Qualitative theory for ordinary differential equations and inclusionsAnichini, Bisconti, Conti, Matucci, Spadini, Villari, Zecca
Boundary value problems on compact and noncompact intervalsAnichini, Conti, Matucci, Pera, Villari, Zecca
Functional differential and differential-difference equations and inclusionsMatucci, Pera, Villari, Zecca
Topological methods for ordinary differential equations and inclusionsAnichini, Bisconti, Conti, Matucci, Pera, Spadini, Villari, Zecca,
Non-autonomous dynamics: non-autonomous dynamical systems and ergodic theoryFabbri
Topological dynamics: Lypaunov exponents, exponential dychotomies and rotation numbersFabbri
Non autonomous Hamiltonian systems, quasi-periodic Schroedinger operatorsFabbri
Bifurcation theoryFabbri