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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians
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by Yoshikazu Giga, Przemysław Górka and Piotr Rybka PDF
Proc. Amer. Math. Soc. 139 (2011), 1777-1785 Request permission


We show a comparison principle for viscosity super- and subsolutions to Hamilton-Jacobi equations with discontinuous Hamiltonians. The key point is that the Hamiltonian depends upon $u$ and has a special structure. The supersolution must enjoy some additional regularity.
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Additional Information
  • Yoshikazu Giga
  • Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Tokyo 153-8914, Japan
  • MR Author ID: 191842
  • Email:
  • Przemysław Górka
  • Affiliation: Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile – and – Department of Mathematics and Information Sciences, Warsaw University of Technology, pl. Politechniki 1, 00-661 Warsaw, Poland
  • Email:
  • Piotr Rybka
  • Affiliation: Institute of Applied Mathematics and Mechanics, Warsaw University, l. Banacha 2, 07-097 Warsaw, Poland
  • Email:
  • Received by editor(s): February 19, 2010
  • Received by editor(s) in revised form: May 23, 2010
  • Published electronically: October 20, 2010
  • Additional Notes: The work of the first author was partly supported by a Grant-in-Aid for Exploratory Research (20654017) and a Grant-in-Aid for Scientific Research (S) (21224001) from the Japan Society for the Promotion of Science
    The second and third authors were partly supported by the Polish Ministry of Science grant N N2101 268935. The second author also enjoyed partial support from Fondecyt 3100019.
    The third author thanks Hokkaido University for its hospitality, as part of the research was performed while he was visiting the university. His work has been partially supported also by FONDAP-Chile
  • Communicated by: Matthew J. Gursky
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 1777-1785
  • MSC (2010): Primary 49L25
  • DOI:
  • MathSciNet review: 2763765