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

Souganidis, P. E.

doi:10.1090/S0002-9939-1986-0818466-4

A remark about viscosity solutions of Hamilton-Jacobi equations at the boundary
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Proc. Amer. Math. Soc. 96 (1986), 323-329 Request permission

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].

References

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