Scale-integration and scale-disintegration in nonlinear homogenization (Q1047936)

After introducing the reader to his concepts of scale transformations (scale-integration and scale-disintegration), the author deals with the homogenization of a nonlinear PDE model arising in magnetostatics. Basically, a class of coarse-scale problems is derived by integrating a family of two-scale minimization problems (scale-integration) in the presence of appropriate orthogonality conditions. By showing that any solution of the coarse-scale problem can be represented as the fine-scale average of a solution of the two-scale problem (scale-disintegration), the author ensures the equivalence of the two formulations mentioned above.