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

Jensen, R.; Souganidis, P. E.

doi:10.1090/S0002-9947-1987-0879566-1

A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension
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by R. Jensen and P. E. Souganidis PDF

Trans. Amer. Math. Soc. 301 (1987), 137-147 Request permission

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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Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation

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