Hamilton-Jacobi Equations With Singular Boundary Conditions on a free Boundary and Applications to Differential Games
Open Access
- 1 May 1991
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 325 (1) , 205-229
- https://doi.org/10.2307/2001667
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.Keywords
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