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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00016270Date
2008Journal name
Archive for Rational Mechanics and AnalysisVolume
187Number
1Publisher
Springer
Pages
49-89
Publication identifier
Metadata
Show full item recordAbstract (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; coercivityRelated items
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