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Transactions of the American Mathematical Society

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


Authors: Martino Bardi and Pierpaolo Soravia
Journal: Trans. Amer. Math. Soc. 325 (1991), 205-229
MSC: Primary 49L10; Secondary 90D25
DOI: https://doi.org/10.1090/S0002-9947-1991-0991958-X
MathSciNet review: 991958
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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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DOI: https://doi.org/10.1090/S0002-9947-1991-0991958-X
Article copyright: © Copyright 1991 American Mathematical Society