Archive for Rational Mechanics and Analysis

, Volume 187, Issue 1, pp 49–89 | Cite as

Homogenization of First-Order Equations with \((u/\varepsilon)\) -Periodic Hamiltonians. Part I: Local Equations

  • Cyril ImbertEmail author
  • Régis Monneau


In this paper, we present a result of homogenization of first-order Hamilton–Jacobi equations with (\(u/\varepsilon\))-periodic Hamiltonians. On the one hand, under a coercivity assumption on the Hamiltonian (and some natural regularity assumptions), we prove an ergodicity property of this equation and the existence of nonperiodic approximate correctors. On the other hand, the proof of the convergence of the solution, usually based on the introduction of a perturbed test function in the spirit of Evans’s work, uses here a twisted perturbed test function for a higher-dimensional problem.


Viscosity Solution Comparison Principle Jacobi Equation Strong Maximum Principle Coercivity Condition 
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© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Polytech’Montpellier & Institut de mathématiques et de modélisation de MontpellierUMR CNRS 5149, Université Montpellier IIMontpellier cedex 5France
  2. 2.CEREMADE, Université Paris-DauphineParis cedex 16France
  3. 3.CERMICS, Université Paris-EstMarne la Vallée Cedex 2France

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