Stratified materials allowing asymptotically prescribed equipotentials
where Ω is a bounded domain in R , 1<p<∞, L stands for suitable Dirichlet boundary conditions and, for each n∈N, 0<an∈L(Ω). In the applications we have in mind Ω is a conductor, the an represent rapidly oscillating (thermic or electric) conductivity coefficients and we are interested in the possible convergence, as n→∞, of the problems P (an) to some “homogenized” limit problem when an converges to some a∈L∞(Ω) in a suitable sense. In the case N=1 it is well known (cf. [12] for p=2) that if 1/an, 1/a and a are in L∞(Ω) and