- Analysis of Diffuse Interface Models
- Computer Assisted Proofs in PDEs
- Control Theory
- Evolution Equations and Dynamical Systems
- Free Boundary Problems
- Game Theory and Convex Optimization
- Geometric Analysis and Riemannian geometry
- Inverse Problems for Partial Differential Equations
- Mathematical Models for Suspension Bridges
- Noncommutative Analysis
- Nonlinear Diffusions
- Nonlinear Elliptic PDEs and Degenerate Equations
- Shape Optimization
Control Theory (E. Marchini)
Optimal control concerns the determination of control strategies for dynamical systems in order to optimize some measure of best performance. A systematic study of optimal control dates back from around 1960, in aerospace engineering, becoming then a field with applications to different research areas dealing, for instance, with traffic flow, economic systems, chemical reactors. Our research mainly concerns infinite dimensional problems. The general framework of the analysis allows to apply our studies to models involving different type of PDEs, including equation with finite or infinite delay. The problems under investigation are classical, such as existence and regularity results of optimal solutions, non degenerate necessary optimality conditions, regularity properties of the value function. A particular attention is devoted to state constrained control problems, largely employed in applied sciences. The technical tools developed, as neighboring feasible trajectories theorems, are suitable also for constraints having nonsmooth boundary.