Homogenization of the demagnetization field operator in periodically perforated domains (Q2371864)

The demagnetization field operator maps any vector field \(\mathbf{m}\) into a vector field \(\mathbf{h}\) satisfying the system \[ \operatorname{div}\mathbf{h}=-\operatorname{div}\mathbf{m}, \qquad \operatorname{rot}\mathbf{h}=0, \] and with the aid of the Green function of the Laplace operator can be expressed in the form of an integral operator. The main result of the paper is a proposition on the homogenization of this operator which is applied to the nonlinear partial differential equation governing the behaviour of ferromagnetic materials: the Landau-Lifshitz equation in the case of periodically perforated domains.