In this article we describe the crystallization conjecture. It states that, in appropriate physical
conditions, interacting particles always place themselves into periodic configurations …

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 the continuation of a previous paper (H. Knüpfer and CB Muratov, Comm. Pure
Appl. Math. 66 (2013), 1129–1162). We investigate the classical isoperimetric problem …

We consider analytical and numerical aspects of the phase diagram for microphase
separation of diblock copolymers. Our approach is variational and is based upon a density …

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 …

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 …

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 …

Gamow's simple liquid drop model of an atomic nucleus recently captured the attention of
mathematicians and has inspired numerous advances and open questions in geometric and …

We consider a family of interaction functionals consisting of power-law potentials with
attractive and repulsive parts and use the concentration compactness principle to establish …

We consider a non-local isoperimetric problem with a repulsive Coulomb term. In dimension
three, this corresponds to Gamow's famous liquid drop model. We show that, whenever the …