# Homogenization of first order equations with $u/\epsilon$-periodic Hamiltonians. Part I: local equations

Abstract : 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 non periodic 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' work, uses here a twisted perturbed test function for a higher dimensional problem.
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https://hal.archives-ouvertes.fr/hal-00016270
Contributor : Cyril Imbert <>
Submitted on : Tuesday, May 15, 2007 - 2:55:58 PM
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Cyril Imbert, Régis Monneau. Homogenization of first order equations with $u/\epsilon$-periodic Hamiltonians. Part I: local equations. Archive for Rational Mechanics and Analysis, Springer Verlag, 2008, 187, pp.49-89. ⟨10.1007/s00205-007-0074-4⟩. ⟨hal-00016270v3⟩

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