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

Bardi, Martino; Soravia, Pierpaolo

doi:10.1090/S0002-9947-1991-0991958-X

Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games
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by Martino Bardi and Pierpaolo Soravia PDF

Trans. Amer. Math. Soc. 325 (1991), 205-229 Request permission

Abstract:

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 particular a relaxation theorem (weak form of the bang-bang principle) is proved for a class of nonlinear differential games.

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