24 citations · 172 across the 23 of their papers we have counts for
15 papers · 1 filter
Spectral inequalities for weighted -Laplacians via Talenti symmetrization
Giulio Bartoli, Giorgio Saracco
We consider the weighted -Laplacian associated with a measure that is absolutely continuous with respect to the Lebesgue measure on an open connected subset $X\subset\mathbb…
On the -limit of weighted fractional energies
Andrea Kubin, Giorgio Saracco, Giorgio Stefani
Given and a bounded open set with Lipschitz boundary, we study the -convergence of the weighted fractional seminorm \[ [u]_{s,p,f}^p = \in…
Geometric criteria for the existence of capillary surfaces in tubes
Giorgio Saracco
We review some geometric criteria and prove a refined version, that yield existence of capillary surfaces in tubes in a gravity free environment, in the case o…
Cylindrical estimates for the Cheeger constant and applications
Aldo Pratelli, Giorgio Saracco
We prove a lower bound for the Cheeger constant of a cylinder , where is an open and bounded set. As a consequence, we obtain existence of minimizers for the sha…
Isoperimetric sets and -Cheeger sets are in bijection
Marco Caroccia, Giorgio Saracco
Given an open, bounded, planar set , we consider its -Cheeger sets and its isoperimetric sets. We study the set-valued map $\mathfrak{V}:[\frac12,+\infty)\rightarrow\mathcal{…
The isoperimetric problem in d domains without necks
Gian Paolo Leonardi, Giorgio Saracco
We give a complete characterization of all isoperimetric sets contained in a domain of the Euclidean plane, that is bounded by a Jordan curve and satisfies a no-neck property. Furt…
Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants
Vesa Julin, Giorgio Saracco
We provide a quantitative lower bound to the Cheeger constant of a set in both the Euclidean and the Gaussian settings in terms of suitable asymmetry indexes. We provide exampl…
Minimizers of the prescribed curvature functional in a Jordan domain with no necks
Gian Paolo Leonardi, Giorgio Saracco
We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional among subsets of a Jordan domain with no necks o…
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…
A sufficient criterion to determine planar self-Cheeger sets
Giorgio Saracco
We show a sufficient criterion to determine if a planar set is a minimizer of the prescribed curvature functional among all of its subsets. As a special case, we derive a suffi…
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…
Two examples of minimal Cheeger sets in the plane
Gian Paolo Leonardi, Giorgio Saracco
We construct two minimal Cheeger sets in the Euclidean plane, i.e. unique minimizers of the ratio "perimeter over area" among their own measurable subsets. The first one gives a co…
Rigidity and trace properties of divergence-measure vector fields
Gian Paolo Leonardi, Giorgio Saracco
We consider a -rigidity property for divergence-free vector fields in the Euclidean -space, where is a non-negative convex function vanishing only at . We show th…
The Cheeger constant of a Jordan domain without necks
Gian Paolo Leonardi, Robin Neumayer, Giorgio Saracco
We show that the maximal Cheeger set of a Jordan domain without necks is the union of all balls of radius contained in . Here, denotes the Cheeger con…
The prescribed mean curvature equation in weakly regular domains
Gian Paolo Leonardi, Giorgio Saracco
We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the…