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Proceedings of the American Mathematical Society

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A remark about viscosity solutions of Hamilton-Jacobi equations at the boundary


Author: P. E. Souganidis
Journal: Proc. Amer. Math. Soc. 96 (1986), 323-329
MSC: Primary 35F20; Secondary 35L99
MathSciNet review: 818466
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Abstract: We consider viscosity solutions of first-order partial differential equations of Hamilton-Jacobi type in bounded domains. We give criteria which identify boundary points at which the equation is automatically satisfied in the viscosity sense, if it holds in the interior. These complement some recent results of M. G. Crandall and R. Newcomb [3].


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DOI: https://doi.org/10.1090/S0002-9939-1986-0818466-4
Keywords: Hamilton-Jacobi equations, boundary value problems, viscosity solutions
Article copyright: © Copyright 1986 American Mathematical Society