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Uniqueness structure of weakly coupled systems of ergodic problems of Hamilton–Jacobi equations

  • Kengo TeraiEmail author
Article
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Abstract

Here, we address a uniqueness structure of viscosity solutions for ergodic problems of weakly coupled Hamilton–Jacobi systems. In particular, we study comparison principle with respect to generalized Mather measures as a generalization of the result proved by Mitake and Tran, which addressed the case of a single equation. To get the main result, it is important to construct Mather measures effectively. We overcome this difficulty by nonlinear adjoint methods.

Keywords

Hamilton–Jacobi equations Weakly coupled systems Viscosity solutions Nonlinear adjoint methods 

Mathematics Subject Classification

35F21 35A50 37J50 

Notes

Acknowledgements

The author would like to thank Professor Hiroyoshi Mitake for his helpful comments and suggestions. The author also would like to appreciate the referees that each of them read this paper very carefully and give him useful comments kindly.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoTokyoJapan

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