Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems

Diogo Gomes*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

In this paper we apply the theory of viscosity solutions of Hamilton-Jacobi equations to understand the structure of certain Hamiltonian flows. In particular, we describe the asymptotic behavior of minimizing orbits, and prove analogs of the classical Hamilton-Jacobi integrability theory that hold under very general conditions. Then, combining partial differential equations techniques with dynamical systems ideas (Mather measures, ergodicity) we study solutions of time-independent Hamilton-Jacobi equation, namely, uniform continuity, difference quotients and non-uniqueness.

Original languageEnglish (US)
Pages (from-to)345-357
Number of pages13
JournalCalculus of Variations and Partial Differential Equations
Volume14
Issue number3
DOIs
StatePublished - Apr 1 2002

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems'. Together they form a unique fingerprint.

Cite this