Some nonlinear homogenization problems

Abstract

We consider the Dirichlet problem for a second order elliptic equations which is nonlinear with respect to the unknown function and its first derivatives. The nonlinear terms involve nonuniform oscillation characterized by a small parameter ∊. We obtain asymptotic expansions for the solution and prove estimates for the remainder term.

Keywords:

• homogenization
• asymptotic' expansion

AMS:

• 73B27
• 35J25

Additional information

Notes on contributors

O.A. Oleinik

R. Temam

G.A. Yosifian