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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension


Authors: R. Jensen and P. E. Souganidis
Journal: Trans. Amer. Math. Soc. 301 (1987), 137-147
MSC: Primary 35B65; Secondary 35L60
MathSciNet review: 879566
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Abstract: Viscosity solutions of Hamilton-Jacobi equations need only to be continuous. Here we prove that, in the special case of a one-dimensional stationary problem, under quite general assumptions, Lipschitz continuous viscosity solutions have right and left derivatives at every point. Moreover, these derivatives have some kind of continuity properties.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0879566-1
PII: S 0002-9947(1987)0879566-1
Keywords: Hamilton-Jacobi equations, viscosity solutions, regularity
Article copyright: © Copyright 1987 American Mathematical Society