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 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]