Partial differential equations and calculus of variations

Partial Differential Equations and Stochastic Processes play an important role in the modeling of physical, biological and financial phenomena. The web page mathematical-analysis.unimore.it contains the updated information on the research activity of our team. The group of researchers is highly skilled in the following specific research topics:

Special materials and regularity in the Calculus of Variations

• Regularity for minimizers of integrals functional with general growth
• Regularity of solutions to obstacle problems
• Existence and qualitative properties of minimizers of integral functionals on multi-dimensional domains
• Existence and concentration properties of solutions to nonlinear elliptic and higher order equations with critical growth
• Sharp limiting inequalities and existence/non-existence of extremal functions

Mathematical models of Financial Markets

• Stochastic processes and Kolmogorov equations
• Black & Scholes model
• Numerical solutions to Kolmogorov equations
• Skewness and risk measurement

Nonlinear evolution equations and applications

• Analysis of solutions to the Nonlinear Schroedinger Equation with singular, double-well, periodic potentials
• Nonlinear phase-transition models, in particular thermodynamically consistent systems with diffuse interface, arising in Biology
• Porous media models with thermomechanical interactions and phase-transition
• Exact controllability of semilinear equations in Banach spaces
• Tumor growth models

Regularity theory for partial differential equations

• Degenerate Kolmogorov operators
• p-Laplace operators
• Obstacle problem

Staff researchers:
Carlo Benassi, Michela Eleuteri, Stefania Gatti, Luca La Rocca, Maria Manfredini, Stefania Perrotta, Sergio Polidoro, Andrea Sacchetti, Federica Sani, Massimo Villarini.