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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A comparison principle for Hamilton-Jacobi equations with discontinuous Hamiltonians


Authors: Yoshikazu Giga, Przemysław Górka and Piotr Rybka
Journal: Proc. Amer. Math. Soc. 139 (2011), 1777-1785
MSC (2010): Primary 49L25
Published electronically: October 20, 2010
MathSciNet review: 2763765
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Abstract: 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
Email: labgiga@ms.u-tokyo.ac.jp

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: pgorka@mini.pw.edu.pl

Piotr Rybka
Affiliation: Institute of Applied Mathematics and Mechanics, Warsaw University, l. Banacha 2, 07-097 Warsaw, Poland
Email: rybka@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10630-5
PII: S 0002-9939(2010)10630-5
Keywords: Hamilton-Jacobi equation, viscosity solutions, discontinuous Hamiltonian
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.