We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem
used to model microphase separation in diblock copolymer melts. We show that critical …

This paper is concerned with a study of the classical isoperimetric problem modified by an
addition of a nonlocal repulsive term. We characterize existence, nonexistence, and radial …

For \Omega_ε=(0,ε)*(0,1) a thin rectangle, we consider minimization of the two-dimensional
nonlocal isoperimetric problem given by \inf_uE^γ_\Omega_ε(u), where …

We study the ternary Ohta–Kawasaki free energy that has been used to model triblock
copolymer systems. Its one-dimensional global minimizers are conjectured to have cyclic …

A ternary inhibitory system is a three component system characterized by two properties:
growth and inhibition. A deviation from homogeneity has a strong positive feedback on its …

This paper provides a quantitative version of the recent result of Knüpfer and Muratov
(Commun Pure Appl Math 66: 1129–1162, 2013) concerning the solutions of an extension of …

We study an isoperimetric problem the energy of which contains the perimeter of a set,
Coulomb repulsion of the set with itself, and attraction of the set to a background nucleus as …

We study a two-dimensional quaternary inhibitory system. This free energy functional
combines an interface energy favoring micro-domain growth with a Coulomb-type long …

In this paper we collect some new observations about periodic critical points and local
minimizers of a nonlocal isoperimetric problem arising in the modeling of diblock …

We consider isoperimetric problem with a nonlocal repulsive term given by the Newtonian
potential. We prove that regular critical sets of the functional are analytic. This optimal …