Stability of Lamellar Configurations in a Nonlocal Sharp Interface Model

Equilibrium models based on a free energy functional deserve special interest in recent investigations, as their critical points exhibit various pattern structures. These systems are characterized by the presence of coexisting phases, whose distribution results from the competition between short and long-range interactions. This article deals with an energy-driven sharp interface model with long-range interaction being governed by a screened Coulomb kernel. We investigate a number of criteria for the stability of lamellar configurations, as they are indeed strict local minimizers. We also give a sufficient condition to ensure a nontrivial periodic 2D minimal energy configuration.