Optimal transport and variational evolution problems
Research lines:
OPTIMAL MASS TRANSPORTATION Characterizations of optimal transport plans, "Displacement extrapolation", Riemannian structure of Wasserstein spaces, Fokker- Planck and nonlinear diffusion equations (Fokker-Planck equations induced by (semi)convex potentials with arbitrary growth, Diffusion equations with variable (space dependent) coefficients, Fourth order equations related to "quantum drift diffusion models"), Dynamic formulation of intermediate metrics and Beckner inequalities, Stability estimates for isoperimetric and Sobolev inequalities.
EVOLUTION PROBLEMS: METRIC SPACES AND NON CONVEX FUNCTIONALS Gradient flows and quasi-Riemannian metric spaces, "Rate-independent" evolution problems, doubly nonlinear equations and non Euclidean distances, Attractors for gradient flows, Discrete second-order models.
