Martedi’ 14 Novembre 2017 alle ORE 14:30 presso il Dipartimento di Matematica e Fisica dell’Universita’ degli Studi Roma Tre – Largo San Leonardo Murialdo,1 – Pal.C – AULA 311 – il prof. E. Runa (Max-Planck-Institute for Mathematics in the Sciences, Leipzig) terrà il seguente seminario di Fisica Matematica:
Exact periodic stripes for minimizers of a local/non-local interaction functional in general dimension
Abstract. In this talk we will consider a functional consisting of a perimeter term and a non-local term which are in competition. In the discrete setting such functional was introduced by Giuliani, Lebowitz, Lieb and Seiringer. We show that the minimizers of such functional are optimal periodic stripes for both the discrete and continuous setting. In the discrete setting, such behaviour has been shown by Giuliani and Seiringer using different techniques for a smaller range of exponents. One striking feature of the functionals is that the minimizers are invariant under a smaller group of symmetries than the functional itself. In the continuous setting, 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. This model has many similarities with the celebrated Ohta-Kawasaki functional. In particular for Ohta-Kawasaki functional, the minimality of periodic stripes is conjectured. This work is in collaboration with Sara Daneri.