We investigate, under a volume constraint and among sets contained in a Euclidean half-
space, the minimization problem of an energy functional given by the sum of a capillarity …

We consider the minimization problem of the functional given by the sum of the fractional
perimeter and a general Riesz potential, which is one generalization of Gamow's liquid drop …

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 …

We consider a variational problem involving competition between surface tension and
charge repulsion. We show that, as opposed to the case of weak (short-range) interactions …

In this paper, we establish a C 1, α-regularity theorem for almost-minimizers of the functional
F ε, γ= P-γ P ε, where γ∈(0, 1) and P ε is a nonlocal energy converging to the perimeter as ε …

Motivated by Gamow's liquid drop model in the large mass regime, we consider an
isoperimetric problem in which the standard perimeter P (E) is replaced by P (E)-γPε (E) …

In this paper we consider a very general form of a non-local energy in integral form, which
covers most of the usual ones (for instance, the sum of a positive and a negative power) …

We study two non-local variational problems that are characterized by the presence of a
Riesz-like repulsive term that competes with an attractive term. The first functional is defined …

We study two non-local variational problems that are characterized by the presence of a
Riesz-like repulsive term that competes with an attractive term. The first functional is defined …

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