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| HAL: hal-00016270, version 3 |
| DOI: 10.1007/s00205-007-0074-4 |
| Detailed view |  Export this paper |
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| Archive for Rational Mechanics and Analysis 187 (2008) 49-89 |
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| Available versions: | v1 (2005-12-22) | v2 (2006-02-06) | v3 (2007-05-15) |
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| Homogenization of first order equations with $u/\epsilon$-periodic Hamiltonians. Part I: local equations |
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| Cyril Imbert 1Régis Monneau 2 |
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| (2008) |
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| 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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| 1: | Institut de Mathématiques et de Modélisation de Montpellier (I3M) |
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CNRS : UMR5149 – Université Montpellier II - Sciences et Techniques du Languedoc |
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| 2: | Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS) |
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INRIA – Ecole des Ponts ParisTech |
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| Subject | : | Mathematics/Analysis of PDEs |
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| periodic homogenization – Hamilton-Jacobi equations – correctors – perturbed test function – coercivity |
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| hal-00016270, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00016270 | |
| oai:hal.archives-ouvertes.fr:hal-00016270 | |
| From: Cyril Imbert | |
| Submitted on: Tuesday, 15 May 2007 14:55:58 | |
| Updated on: Saturday, 5 January 2008 12:11:19 | |
