Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampére equations. VIASM 2016. Based on lectures at the Rutgers University, NJ, USA, 2013.

*(English)*Zbl 1373.35006
Lecture Notes in Mathematics 2183. Cham: Springer (ISBN 978-3-319-54207-2/pbk; 978-3-319-54208-9/ebook). vii, 228 p. (2017).

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Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton-Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the nonlinear adjoint method, is introduced. The appendix offers a short introduction to the theory of viscosity solutions of first-order Hamilton-Jacobi equations.

Part I and II of this volume will be reviewed individually.

##### MSC:

35-06 | Proceedings, conferences, collections, etc. pertaining to partial differential equations |

35B10 | Periodic solutions to PDEs |

35B40 | Asymptotic behavior of solutions to PDEs |

35B50 | Maximum principles in context of PDEs |

35B51 | Comparison principles in context of PDEs |

35B65 | Smoothness and regularity of solutions to PDEs |

35J40 | Boundary value problems for higher-order elliptic equations |