We obtain a sharp quantitative isoperimetric inequality for nonlocal s-perimeters, uniform
with respect to s bounded away from 0. This allows us to address local and global minimality …

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

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an
interesting problem in the calculus of variations: Find a set Ω⊂R^3 with given volume A that …

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 …

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 …

We consider a class of nonlocal shape optimization problems for sets of fixed mass where
the energy functional is given by an attractive/repulsive interaction potential in powerlaw …

We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z> 0
can bind at most Z+ C electrons, where C is a universal constant. This result is obtained …

Nonexistence of Large Nuclei in the Liquid Drop Model Page 1 DOI 10.1007/s11005-016-0860-8
Lett Math Phys (2016) 106:1033–1036 Nonexistence of Large Nuclei in the Liquid Drop Model …