Homogenization for heat transfer in polycrystals with interfacial resistances

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.

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