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

DOI:
https://doi.org/10.1090/S0002-9939-2010-10630-5

Published electronically:
October 20, 2010

MathSciNet review:
2763765

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Abstract | References | Similar Articles | Additional Information

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 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:
https://doi.org/10.1090/S0002-9939-2010-10630-5

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.