# Some Homogenization Results for Non-Coercive Hamilton-Jacobi Equations

Abstract : Recently, C. Imbert \& R. Monneau study the homogenization of coercive Hamilton-Jacobi Equations with a $u/\e$-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 $u/\e$-dependence) but in the case of {\it non-coercive Hamiltonians}. As a by-product, we obtain a simpler and more natural proof of the results of C. Imbert \& R. Monneau, but under slightly more restrictive assumptions on the Hamiltonians.
Keywords :
Document type :
Journal articles

Cited literature [26 references]

https://hal.archives-ouvertes.fr/hal-00071284
Contributor : Guy Barles <>
Submitted on : Friday, December 22, 2006 - 2:08:07 PM
Last modification on : Saturday, October 26, 2019 - 1:51:19 AM
Long-term archiving on: Monday, September 20, 2010 - 6:13:37 PM

### Files

HomDegV2.pdf
Files produced by the author(s)

### Citation

Guy Barles. Some Homogenization Results for Non-Coercive Hamilton-Jacobi Equations. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2007, 30 (4), pp.449--466. ⟨hal-00071284v2⟩

Record views