# 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.

[Ultimo aggiornamento: 04/02/2021 12:45:53]