5 papers
The $\eps-\eps^β$ property for clusters with double density
A. Pratelli, V. Scattaglia
This article is devoted to extend the "$\eps-\eps^β$ property" to the case of clusters in an Euclidean space with a double density.
Particle approximation of nonlocal interaction energies
Davide Carazzato, Aldo Pratelli, Ihsan Topaloglu
We consider Riesz-type nonlocal energies with general interaction kernels and their discretizations related to particle systems. We prove that the discretized energies -converg…
The isoperimetric inequality for the capillary energy outside convex sets
N. Fusco, V. Julin, M. Morini +1
We study the isoperimetric problem for capillary hypersurfaces with a general contact angle , outside arbitrary convex sets. We prove that the capillary energy of an…
Continuity of critical points for 1-dimensional non-local energies
Davide Carazzato, Nicola Fusco, Aldo Pratelli
In this paper we deal with the bounded critical points of a Riesz energy of attractive-repulsive type in dimension 1. Under suitable assumptions on the growth of the kernel in the…
Connectedness properties of small minimal clusters in Riemannian or Finsler manifolds
Stefano Nardulli, Aldo Pratelli
We prove that in a compact Riemannian manifold, the -minimal clusters of sufficiently small total volume are connected and with small diameter, while in a more general Finsler m…