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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • © 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