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Some homogenization results for non-coercive Hamilton–Jacobi equations

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Abstract

Recently, C. Imbert and R. Monneau study the homogenization of coercive Hamilton–Jacobi Equations with a u/ε-dependence: this unusual dependence leads to a non-standard cell problem and, in order to solve it, they introduce new ideas to obtain the estimates on the oscillations of the solutions. In this article, we use their ideas to provide new homogenization results for “standard” Hamilton–Jacobi Equations (i.e. without a u/ε-dependence) but in the case of non-coercive Hamiltonians. As a by-product, we obtain a simpler and more natural proof of the results of C. Imbert and R. Monneau, but under slightly more restrictive assumptions on the Hamiltonians.

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  1. Laboratoire de Mathématiques et PhysiqueThéorique (UMR CNRS 6083), Fédération Denis Poisson, Université François Rabelais de Tours, Parc de Grandmont, 37200, Tours, France

    Guy Barles

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  1. Guy Barles
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Correspondence to Guy Barles.

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Barles, G. Some homogenization results for non-coercive Hamilton–Jacobi equations. Calc. Var. 30, 449–466 (2007). https://doi.org/10.1007/s00526-007-0097-6

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  • DOI: https://doi.org/10.1007/s00526-007-0097-6

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