Calculus of Variations and Geometric Measure Theory

M. Bonacini - H. Knüpfer

Ground states of a ternary system including attractive and repulsive Coulomb-type interactions

created by bonacini on 06 Dec 2015
modified on 26 Sep 2016


Published Paper

Inserted: 6 dec 2015
Last Updated: 26 sep 2016

Journal: Calc. Var. Partial Differential Equations
Volume: 55
Number: 5
Year: 2016
Doi: 10.1007/s00526-016-1047-y


We study a variational model where two interacting phases are embedded in a third neutral phase. The energy of the system is the sum of a local interfacial contribution and a nonlocal interaction of Coulomb type. Such models are e.g. used to describe systems of copolymer-homopolymer blends or of surfactants in water solutions. We establish existence and regularity properties of global minimizers, together with a full characterization of minimizers in the small mass regime. Furthermore, we prove uniform bounds on the potential of minimizing configurations, which in turn imply some qualitative estimates about the geometry of minimizers in the large mass regime. One key mathematical difficulty in the analysis is related to the fact that two phases have to be minimized simultaneously with both attractive and repulsive interaction present.