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

DOI:
https://doi.org/10.1090/S0002-9939-1986-0818466-4

MathSciNet review:
818466

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Abstract | References | Similar Articles | Additional Information

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**].

**[1]**M. G. Crandall, L. C. Evans and P.-L. Lions,*Some properties of viscosity solutions of Hamilton-Jacobi equations*, Trans. Amer. Math. Soc.**282**(1984), 487-502. MR**732102 (86a:35031)****[2]**M. G. Crandall and P.-L. Lions,*Viscosity solutions of Hamilton-Jacobi equations*, Trans. Amer. Math. Soc.**277**(1983), 1-42. MR**690039 (85g:35029)****[3]**M. G. Crandall and R. Newcomb,*Viscosity solutions of Hamilton-Jacobi equations at the boundary*, Proc. Amer. Math. Soc.**94**(1985), 283-290. MR**784180 (86f:35047)****[4]**M. G. Crandall and P. E. Souganidis,*Developments in the theory of nonlinear first-order partial differential equations*(Proc. Internat. Sympos. on Differential Equations, Birmingham, Alabama, 1983, I. W. Knowles and R. T. Lewis, eds.), North-Holland, Amsterdam, 1984. MR**799343 (86j:35033)****[5]**L. C. Evans,*Some max-min methods for the Hamilton-Jacobi equation*, Indiana Univ. Math. J.**33**(1984), 31-50. MR**726105 (85b:35009)****[6]**P.-L. Lions,*Generalized solutions of Hamilton-Jacobi equations*, Pitman, Boston, Mass., 1982. MR**667669 (84a:49038)**

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Additional Information

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