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

Imbert, Cyril; Monneau, Régis (2008), Homogenization of First-Order Equations with (u/ε) -Periodic Hamiltonians. Part I: Local Equations, Archive for Rational Mechanics and Analysis, 187, 1, p. 49-89. http://dx.doi.org/10.1007/s00205-007-0074-4

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00016270
Date
2008
Journal name
Archive for Rational Mechanics and Analysis
Volume
187
Number
1
Publisher
Springer
Pages
49-89
Publication identifier
http://dx.doi.org/10.1007/s00205-007-0074-4
Metadata
Show full item record
Author(s)
Imbert, Cyril cc
Monneau, Régis
Abstract (EN)
In this paper, we present a result of homogenization of first-order Hamilton–Jacobi equations with ( u/ε )-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.
Subjects / Keywords
periodic homogenization; Hamilton-Jacobi equations; correctors; perturbed test function; coercivity

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