Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games

Martino Bardi, Pierpaolo Soravia
1991 Transactions of the American Mathematical Society  
A class of Hamilton-Jacobi equations arising in generalized timeoptimal control problems and differential games is considered. The natural global boundary value problem for these equations has a singular boundary condition on a free boundary. The uniqueness of the continuous solution and of the free boundary is proved in the framework of viscosity solutions. A local uniqueness theorem is also given, as well as some existence results and several applications to control and game theory. In
more » ... lar a relaxation theorem (weak form of the bang-bang principle) is proved for a class of nonlinear differential games.
doi:10.1090/s0002-9947-1991-0991958-x fatcat:tsyvvwh6x5b6rhe77f3fa4vnj4