Homogenization of quasilinear elliptic equations with non-uniformly bounded coefficients
Brahim Amaziane, Leonid Pankratov, Andrey Lvovich Piatnitski · Nonlinearity · 2006
The goal of the paper is to study the asymptotic behaviour of solutions to a high contrast quasilinear equation of the form −div (|∇u e | p−2 ∇u e ) + G e (x)|u e | p−2 u e = f( x) in �, where � ⊂ R n with n 2, 1 <p n, and the coefficient G e (x) is assumed to blow up as e → 0 on a set of Ne isolated inclusions of asymptotically small measure. Here Ne −→ +∞ as e → 0. It is shown that the asymptotic behaviour, as e → 0, of the solution u e is described in terms of a homogenized quasilinear equation of the form −div (|∇u| p−2 ∇u) + B(x)|u| p−2 u = f( x) in �, where the coefficient B(x) is calculated as a local energy characteristic of the microstructure associated with the potential G e (x) in the original problem. This