Homogenization of Quasilinear Parabolic Equations in Periodic Media†

^†Dedicated to Professor Yves Meyer with our best wishes in his retirement.

Abstract

We study the homogenization of the nonlinear parabolic equation,

where , a.e. (y, s). We will consider the homogenization as a viscosity process.

^†Dedicated to Professor Yves Meyer with our best wishes in his retirement.

Keywords:

• Homogenization
• Nonlinear parabolic equations
• Viscosity solutions

Acknowledgments

First and third authors partially supported by Project BFM2001-0183 of the M.C.Y.T. (Spain). The second author was partially supported by Programa Iberdrola de Profesores Visitantesand NSF grant DMS-0070648. We like to thank Professors L. A. Caffarelli and L. C. Evans for useful conversations and correspondence concerning the contents of this article.

Notes

^†Dedicated to Professor Yves Meyer with our best wishes in his retirement.

^aIf uwere not a viscosity subsolution, then the proof of Theorem II.1 is basically the same with the auxiliary functions changed in accordance with Remark IV.7, and making appropriate changes in the signs