6 papers · 1 filter
Nonexistence for screened Hartree energies
Dario Mazzoleni, Riccardo Moraschi, Berardo Ruffini
We develop an anti-concentration method for volume-constrained nonlocal shape optimization. Precisely, we apply it to prove the nonexistence of minimizers of an optimal design prob…
Existence and Regularity in the Small-Mass Regime for a Hartree--Ohta-Kawasaki Shape Optimization Problem
Dario Mazzoleni, Riccardo Moraschi, Berardo Ruffini
We consider a shape optimization problem for a hybrid energy combining local confinement and nonlocal Coulomb repulsion. Specifically, for any open set o…
Barycentric stability of nonlocal perimeters: the convex case
Chiara Gambicchia, Enzo Maria Merlino, Berardo Ruffini +1
In this work, we establish a sharp form of a nonlocal quantitative isoperimetric inequality involving the barycentric asymmetry for convex sets. This result can be seen as the nonl…
A strong quantitative form of the fractional isoperimetric inequality
Eleonora Cinti, Enzo Maria Merlino, Berardo Ruffini
We show a strong version of the fractional quantitative isoperimetric inequality, in which the isoperimetric deficit controls not only the Fraenkel asymmetry but also a sort of osc…
Threshold dynamics approximation schemes for anisotropic mean curvature flows with a forcing term
Bohdan Bulanyi, Berardo Ruffini
We establish the convergence of threshold dynamics-type approximation schemes to propagating fronts evolving according to an anisotropic mean curvature motion in the presence of a…
An optimal design problem for a charge qubit
Dario Mazzoleni, Cyrill B. Muratov, Berardo Ruffini
In this paper we introduce a simple variational model describing the ground state of a superconducting charge qubit. The model gives rise to a shape optimization problem that aims…