On the $\Gamma$-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part III: The energies with non local terms

Abstract

We use the technique developed in [32]-[33] to construct the upper and the lower bounds for classes of problems containing non-local terms, including problems in micromagnetics and problems arising in the variational study of the Method of Vanishing Viscosity for systems of conservation laws. We reduced these problems to the problems considered in [32]-[33], with the appropriate prescribed differential constraint.

arXiv commentarXiv admin note: text overlap with arXiv:1112.2968, arXiv:1112.2305