6 papers · 1 filter
Minimality of balls in the small volume regime for a general Gamow type functional
Davide Carazzato, Nicola Fusco, Aldo Pratelli
We consider functionals given by the sum of the perimeter and the double integral of some kernel , multiplied by a "mass parameter" $…
Minimisers of a general Riesz-type Problem
Matteo Novaga, Aldo Pratelli
We consider sets in which minimise, for fixed volume, the sum of the perimeter and a non-local term given by the double integral of a kernel $g:\mathbb R^N\setminus\{…
Sharp quantitative stability for isoperimetric inequalities with homogeneous weights
Eleonora Cinti, Federico Glaudo, Aldo Pratelli +2
We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homog…
The property in the isoperimetric problem with double density, and the regularity of isoperimetric sets
Aldo Pratelli, Giorgio Saracco
We prove the validity of the property in the isoperimetric problem with double density, generalising the known properties for the case of single density…
On the isoperimetric problem with double density
Aldo Pratelli, Giorgio Saracco
In this paper we consider the isoperimetric problem with double density in an Euclidean space, that is, we study the minimisation of the perimeter among subsets of w…
The closure of planar diffeomorphisms in Sobolev spaces
Guido De Philippis, Aldo Pratelli
We characterize the (sequentially) weak and strong closure of planar diffeomorphisms in the Sobolev topology and we show that they always coincide. We also provide some sufficient…