First and second order Hamilton-Jacobi equations for state-constrained control problems (Reference: ESR3) ****** this position has been filled ******

Descritpion of the subject: The formulation of optimal control problems involving realistic models typically involves constraints on control and state variables, to take account of a target to be reached, mechanical or thermal constraints, obstacles, etc. When constraints are present and when, as is often the case, rather severe controllability conditions are not satisfied, it is known that the value function may be discontinuous. However the nature of its possible discontinuities are not well understood. Discontinuities in the system equations also give rise to discontinuous value functions. This  research aims to provide a detailed characterization of value functions as discontinuous viscosity and bilateral solutions of Hamilton-Jacobi equations, for a broad class of optimal control problems involving constraints, unbounded controls, stochastic models and discontinuous coefficients. We aim also to investigate the regularity of the value function along optimal trajectories for a number of optimal control problems of interest, including that of minimizing the distance function along geodesics.