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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 12:45:30]