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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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Keywords: Hamilton-Jacobi equations, viscosity solutions, regularity
Article copyright: © Copyright 1987 American Mathematical Society