Abstract
Heat conduction is investigated in periodic (single- or multi-phase) microstructures having disconnected phases and resistances on the interfaces between the phases. After deriving uniform a priori estimates for the microsolutions the macroscopic equations are obtained rigorously by means of two-scale convergence. The required generalization of two scale convergence for surfaces is shown with the help of a Weyl decomposition in the context of Sobolev spaces with respect to measures.