Inserted: 4 apr 2017
Last Updated: 10 apr 2017
We study the functional considered in 13,14,16 and a continuous version of it, analogous to the one considered in 18. The functionals consist of a perimeter term and a non-local term which are in competition. For both the continuous and discrete problem, we show that the global minimizers are exact periodic stripes. One striking feature of the functionals is that the minimizers are invariant under a smaller group of symmetry than the functional itself. To our knowledge this is the first example of a model with local-nonlocal terms in competition such that the functional is invariant under permutation of coordinates and the minimizers display a pattern formation which is one dimensional.