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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- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 301 (1987), 137-147
- MSC: Primary 35B65; Secondary 35L60
- DOI: https://doi.org/10.1090/S0002-9947-1987-0879566-1
- MathSciNet review: 879566