ON THE HOMOGENIZATION OF THE RECTANGULAR DAM PROBLEM
Marco Codegone, José Francisco Rodrigues · PORTO Publications Open Repository TOrino (Politecnico di Torino) · 1981
Summary: Using the variational inequality formulation we study the homogenization of the dam problem with variable permeability in the special case where k(x, y) = = k\(x)k.2(y). This includes the cases of vertical and horizontal layers. In the limit we obtain the classical homogeneous problem of Baiocchj. From the Hausdorff convergence of the coincidence sets we obtain the uniform convergence of the free boundaries in the case where they have not inflection points. In the general one still has the convergence in mean of the free boundaries as a consequence of the con vergence in measure of the coincidence sets.