Ricerca Settori DisciplinariAnalisi Matematica

Analisi Matematica

Faculty staff

Post-docs

Carlo Alberto Antonini
Tianrui Dai

PhD Students

Francesco Colasanto
Gabriele Giannone
Igor Pereira Pinhero

Research topics

Calculus of Variations

The Calculus of Variations typically deals with minimization problems for functionals defined on classes of functions. Some relevant related topics are geometric measure theory, partial differential equations, geometric inequalities, local and nonlocal operators. In particular we study applications to interfaces and microstructures, shape optimization, evolutions of defects in materials, Density Functional Theory.

Existence and regularity of solutions to variational problems
Optimal transport problems
Free discontinuity and free boundary problems
Variational solutions to evolutionary problems
Optimization problems

People: Luigi De Pascale, Matteo Focardi, Gianmarco Giovannardi, Giuliano Lazzaroni, Giorgio Saracco, Paolo Marcellini, Vincenzo Vespri

Some former members: Elvira Mascolo

Some external collaborators: Guillaume Carlier (Université Paris Dauphine, France), Thierry Champion (Université de Toulon, France), Sergio Conti (Universität Bonn, Germany), Camillo De Lellis (IAS, Princeton, USA), Emanuele Spadaro (Sapienza Università di Roma), Caterina Zeppieri (Universität Münster, Germany)

Mathematical Control Theory

Mathematical Control Theory is a wide branch of mathematics that studies how and to what extent it is possible to influence the behavior of a system evolving in time so as to achieve a desired goal. The expertise of the group is in the analysis of nonlinear systems in finite dimensional spaces and manifolds, as well as of (linear and nonlinear) evolutionary PDE. The methods employed range from differential geometry to functional analysis and semigroup theory, PDE methods, dynamical systems theory. Specifically, the topics and related research work include:

Geometric Control for infinite dimensional systems and for PDE,
Approximate controllability in spaces of curves; control of complexes;
Optimal Control theory for ordinary differential equations (ODE) and PDE: in particular,

- nonlinear systems with generalized controls and generalized minimizers in noncoercive variational problems;
- the Linear-Quadratic problem and Riccati equations with unbounded coefficients;
- sufficient optimality conditions for Pontryagin extremals and structural stability of locally optimal trajectories in optimal control problems for ODE;
Control-theoretic properties of nonautonomous linear control systems.

People: Francesca Bucci, Roberta Fabbri, Laura Poggiolini

Some former members: Gianna Stefani, Pietro Zecca
Some external collaborators: Andrey Agrachev (SISSA), Paolo Acquistapace (Università di Pisa), Francesca Carlotta Chittaro (Université de Toulon, France), Matthias Eller (Georgetown University, Washington DC, USA), Manuel Guerra (ISEG, Portugal), Carmen Nunez (Universidad de Valladolid, Spain)

Partial differential equations

The world of Partial Differential Equations is a wide area of Mathematical Analysis. We mainly focus on its connection with Calculus of Variations, functional inequalities, geometric analysis, convexity, inverse problems, control theory, dynamical systems and fluid dynamics. The main themes of research activity are:

Existence and regularity theory
Qualitative properties of solutions to elliptic equations
Inverse problems and applications
Parabolic and hyperbolic equations, coupled systems
Geometric and functional inequalities
Convex geometry, analytic aspects of convexity, and applications

People: Gabriele Bianchi, Chiara Bianchini, Luca Bisconti, Francesca Bucci, Andrea Cianchi, Andrea Colesanti, Elisa Francini, Gianmarco Giovannardi, Alessandro Goffi, Marco Longinetti, Giorgio Saracco, Rolando Magnanini, Paolo Salani, Sergio Vessella

Some former members: Giorgio Talenti

Some external collaborators: Paolo Acquistapace (Università di Pisa), Andrea Aspri (Università di Milano), Lorenzo Baldassari (Rice University, Houston, USA), Elena Beretta (NYU Abu Dhabi, United Arab Emirates), Diego Berti (Università di Torino), Davide Catania (Università eCampus), Dominic Breit (Universität Clausthal, Germania), Martin de Hoop (Rice University, Houston, USA) Lars Diening (Universität Bielefeld, Germania), Federica Dragoni (Cardiff University, UK), Matthias Eller (Georgetown University, Washington DC, USA), Richard Gardner (Western Washington University, USA), Antoine Henrot (IECL, Université de Lorraine, Nancy, France), Kazuhiro Ishige (The University of Tokyo, Japan), Toru Kan (Osaka Prefecture University, Japan), Qing Liu (Okinawa Institute of Science and Technology, Japan), Monika Ludwig (Technische Universität, Vienna, Austria), Michele Marini (Università del Sannio), Antonino Morassi (Università di Udine), Michiaki Onodera (Tokyo Institute of Technology, Japan), Lubos Pick (Charles University, Prague, Czech Republic), Giorgio Poggesi (University of Western Australia), Edi Rosset (Università di Trieste), Shigeru Sakaguchi (Tohoku University, Japan), Sebastian Schwarzacher (University of Uppsala, Sweden), Eva Sincich (Università di Trieste), Lenka Slavikova (Charles University, Prague, Czech Republic), Asuka Takatsu (Tokyo Metropolitan University, Japan), Jenn-Nan Wang (National Taiwan University)

ODE’s and Dynamical Systems

Ordinary differential equations (ODEs) is a well developed field in mathematics. Due to its broad applications in many areas of mathematics, science and technology, its modern branches are still actively developing. The modern theory of ODEs makes use of different and complementary approaches and tools, and also include the dynamical systems techniques. In particular with the term “nonautonomous dynamics” we refer to the systematic use of dynamical tools to study the solutions of differential or difference equations whose coefficients are time dependent. The time dependence may range from periodicity to the most extreme one, passing through Bohr almost periodicity, Birkhoff and Poisson to stochasticity.

In particular, we focus on

Almost everywhere Lyapunov exponents, exponential splittings, rotation numbers, theory of cocycles.
Boundary value problems for differential and difference equations, oscillation and asymptotic behavior and stability of solutions.
Navier Stokes equations and related problems.
Nonautonomous bifurcation.
Nonautonomous linear Hamiltonian systems.
Semigroups and evolution operators.
Topological methods for ODEs, functional differential equations with delay, integro-differential equations and inclusions.

People: Luca Bisconti, Roberta Fabbri, Massimo Furi, Serena Matucci, Maria Patrizia Pera, Marco Spadini, Gabriele Villari

Some former members: Giuseppe Anichini, Russell Johnson, Mauro Marini

Some external collaborators: Pierluigi Benevieri (Universidade de Sao Paulo, Brasil), Diego Berti (Università di Pisa), Alessandro Calamai, (Università Politecnica delle Marche, Ancona), Davide Catania (Università eCampus), Zuzana Došla (Masaryk University, Czech Republic), Cinzia Elia (Università di Bari), Gennaro Infante (Università della Calabria), Paolo Maria Mariano (DICEA, Università di Firenze), Carmen Nunez, (Universidad de Valladolid, Spain), Pavel Řehàk (BUT, Czech Republic), Paola Rubbioni, (Università di Perugia), Peter Sepitka (Masaryk University, Czech Republic)

Seminars

Ultimo aggiornamento

09.04.2025