Paola Mannucci

Nonzero-Sum Stochastic Differential Games with Discontinuous Feedback

The existence of a Nash equilibrium feedback is established for a two-player nonzero-sum stochastic differential game with discontinuous feedback. This is obtained by studying a parabolic system strongly coupled by discontinuous terms.

Comparison principles and Dirichlet problem for fully nonlinear degenerate equationsof Monge–Ampère type

Abstract. We study fully nonlinear partial differential equations of Monge–Ampère type involving the derivatives with respect to a family of vector fields. The main result is a comparison principle among viscosity subsolutions, convex with respect to , and viscosity supersolutions (in a weaker sense than usual), which implies the uniqueness of solution to the Dirichlet problem. Its assumptions include the equation of prescribed horizontal Gauss curvature in Carnot groups. By the Perron method we also prove the existence of a solution either under a growth condition of the nonlinearity with respect to the gradient of the solution, or assuming the existence of a subsolution attaining continuously the boundary data, therefore generalizing some classical result for Euclidean Monge–Ampère equations.

A free boundary problem in an absorbing porous material with saturation dependent permeability

Abstract. We prove a well posedness result for a free boundary problem describing the filtration of an incompressible viscous fluid in a porous medium containing water absorbing granules.¶The location of the wetting front (the free boundary) is described by a Stefan like problem for a parabolic equation which is coupled with an hyperbolic equation describing the absorption kinetic of the granules.

Some existence theorems for an N -dimensional parabolic equation with a discontinuous source term

The authors consider an n-dimensional semilinear equation of parabolic type with a discontinuous source term arising from combustion theory. The authors prove a local existence for a classical solution having a “regular” free boundary. In this regard, the free boundary is a surface through which the discontinuous source term exhibits a switch-like behaviour. The authors specify conditions under which this solution and its free boundary are global in time. The authors also prove uniqueness and continuous dependence theorems.

STUDY OF THE MATHEMATICAL MODEL FOR A POLYMERIZATION PROBLEM

We analyze a mathematical model for a problem concerning the cementation of an endomedullary infibulum. The cement used is a polymer that solidifies in situ generating heat. We consider a problem in cylindrical symmetry in which the degree of polymerization and the temperature are the unknown functions. We prove the existence and uniqueness of a classical solution global in time.

Stochastic Homogenization for Functionals with Anisotropic Rescaling and Noncoercive Hamilton--Jacobi Equations

We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable. We look at Hamiltonians like

Nash Points for Nonzero-Sum Stochastic Differential Games with Separate Hamiltonians

H(x,\sigma(x)p,\omega)

On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations

where

Viscosity solutions for elliptic-parabolic problems

\sigma(x)

The Dirichlet problem for fully nonlinear elliptic equations non-degenerate in a fixed direction

is a matrix associated to a Carnot group. The rescaling considered is consistent with the underlying Carnot group structure, thus anisotropic. We will prove that under suitable assumptions for the Hamiltonian, the solutions of the