Calculus of Variations and Geometric Measure Theory

M. Cicalese - L. De Luca - M. Novaga - M. Ponsiglione

Ground States of a two phase model with cross and self attractive interactions

created by deluca on 30 Jul 2015
modified on 29 Oct 2016


Published Paper

Inserted: 30 jul 2015
Last Updated: 29 oct 2016

Journal: SIAM J. Math. Anal.
Volume: 48
Number: 5
Pages: 3412-3443
Year: 2016


We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, di erent behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state con gurations.

Keywords: Variational methods, shape optimization, nonlocal interactions, Coulomb interactions