Homogenization of a class of quasilinear elliptic equations in high-contrast fissured media

The aim of the paper is to study the asymptotic behaviour of the solution of a quasilinear elliptic equation of the form -div (a(epsilon)(x) vertical bar del u(epsilon)vertical bar(p-2)del mu(epsilon)) + g(x)vertical bar mu(epsilon)vertical bar(p-2)mu(epsilon) = S-epsilon(x) in ohm, with a high-contrast discontinuous coefficient a(epsilon)(x), where E is the parameter characterizing the scale of the microstucture. The coefficient a(epsilon)(x) is assumed to degenerate everywhere in the domain ohm except in a thin connected microstructure of asymptotically small measure. It is shown that the asymptotical behaviour of the solution u(epsilon) as epsilon -> 0 is described by a homogenized quasilinear equation with the coefficients calculated by local energetic characteristics of the domain ohm.