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

Cyril Imbert (1) , Régis Monneau (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

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.

Mots clés: periodic homogenization; Hamilton-Jacobi equations; correctors; perturbed test function; coercivity

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Régis Monneau. Homogenization of first order equations with $u/\epsilon$-periodic Hamiltonians. Part I: local equations. 2006. ⟨hal-00016270v2⟩