According to the classical theory of Weiss, Landau, and Lifshitz, on a microscopic scale a ferromagnetic body is magnetically saturated (i.e., \M\ = M: constant) and consists of regions in which the magnetization is uniform, separated by thin transition layers. Any stationary configuration corresponds to a minimum point of an energy functional in which a small parameter epsilon is present. The asymptotic behaviour as epsilon --> 0 is studied here. It is easy to see that any sequence of minimizers contains a subsequence M-epsilon(j) that converges to a field M. By means of a GAMMA-limit procedure it is shown that this field M is a minimizer of a new functional containing a term proportional to the area of the surfaces separating different domains of uniform magnetization. The C1,gamma-regularity of these surfaces, for gamma < 1/2, is also proved under suitable assumptions for the external magnetic field.
