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 …

If the Coulomb term is not present in (1.1) and (1.3), a standard Modica-Mortola type result
establishes a link between the two functional through Gamma convergence when the …

We consider a nonlocal isoperimetric problem defined in the whole space R^N, whose
nonlocal part is given by a Riesz potential with exponent α∈(0,N-1). We show that critical …

We give a detailed description of the geometry of single‐droplet patterns in a nonlocal
isoperimetric problem. In particular, we focus on the sharp interface limit of the Ohta …

This paper is concerned with the macroscopic behavior of global energy minimizers in the
three-dimensional sharp interface unscreened Ohta–Kawasaki model of diblock copolymer …

This paper presents a two-dimensional investigation of the phase diagram for global
minimizers to a Cahn–Hilliard functional with long-range interactions. Based upon the H^-1 …

We establish the behavior of the energy of minimizers of non-local Ginzburg-Landau
energies with Coulomb repulsion in two space dimensions near the onset of multi-droplet …

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 …

This is the second in a series of papers in which we derive a Γ-expansion for the two-
dimensional non-local Ginzburg–Landau energy with Coulomb repulsion known as the Ohta …