37 citations · 71 across the 19 of their papers we have counts for
25 papers
Some remarks on nonexistence in the Gamow liquid drop model
Dario Mazzoleni, Aldo Pratelli, Berardo Ruffini
In this paper we deal with the celebrated Gamow liquid drop model, namely, for , and , we study the problem \[ \min\Big\{P(Ω)+ V_α(Ω) : Ω\subset \mathbb{…
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 of…
Free boundary regularity for a spectral optimal partition problem with volume and inclusion constraints
Dario Mazzoleni, Makson S. Santos, Hugo Tavares
This paper is devoted to a complete characterization of the free boundary of all solutions to the following spectral -partition problem with measure and inclusion constraints: \…
Asymptotic location and shape of the optimal favorable region in a Neumann spectral problem
Lorenzo Ferreri, Dario Mazzoleni, Benedetta Pellacci +1
We complete the study concerning the minimization of the positive principal eigenvalue associated with a weighted Neumann problem settled in a bounded regular domain $Ω\subset \mat…
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…
On a degenerate second order traffic model: existence of discrete evolutions, deterministic many-particle limit and first order approximation
Dario Mazzoleni, Emanuela Radici, Filippo Riva
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second ord…
On the dimension of the singular set in optimization problems with measure constraint
Dario Mazzoleni, Giorgio Tortone, Bozhidar Velichkov
In this paper, we prove estimates on the dimension of the singular part of the free boundary for solutions to shape optimization problems with measure constraints. The focus is on…
Regularity of the optimal sets for a class of integral shape functionals
Giuseppe Buttazzo, Francesco Paolo Maiale, Dario Mazzoleni +2
We prove {the first} regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the energy of a domain is ob…
-Gradient Flows of Spectral Functionals
Dario Mazzoleni, Giuseppe Savaré
We study the -gradient flow of functionals depending on the eigenvalues of Schrödinger potentials for a wide class of differential operators associated to clo…
Singular analysis of the optimizers of the principal eigenvalue in indefinite weighted Neumann problems
Dario Mazzoleni, Benedetta Pellacci, Gianmaria Verzini
We study the minimization of the positive principal eigenvalue associated to a weighted Neumann problem settled in a bounded smooth domain , within a suita…
Regularity of the optimal sets for the second Dirichlet eigenvalue
Dario Mazzoleni, Baptiste Trey, Bozhidar Velichkov
This paper is dedicated to the regularity of the optimal sets for the second eigenvalue of the Dirichlet Laplacian. Precisely, we prove that if the set minimizes the functional…
A spectral shape optimization problem with a nonlocal competing term
Dario Mazzoleni, Berardo Ruffini
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Dirichlet Laplacian and the relative strength of a Riesz-type interaction function…
On principal frequencies, volume and inradius in convex sets
Lorenzo Brasco, Dario Mazzoleni
We provide a sharp double-sided estimate for Poincaré-Sobolev constants on a convex set, in terms of its inradius and dimensional measure. Our results extend and unify previous…
Optimization results for the higher eigenvalues of the -Laplacian associated with sign-changing capacitary measures
Marco Degiovanni, Dario Mazzoleni
In this paper we prove the existence of an optimal set for the minimization of the -th variational eigenvalue of the -Laplacian among -quasi open sets of fixed measure inc…
Quantitative analysis of a singularly perturbed shape optimization problem in a polygon
Dario Mazzoleni, Benedetta Pellacci, Gianmaria Verzini
We carry on our study of the connection between two shape optimization problems with spectral cost. On the one hand, we consider the optimal design problem for the survival thresho…
Asymptotic spherical shapes in some spectral optimization problems
Dario Mazzoleni, Benedetta Pellacci, Gianmaria Verzini
We study the optimization of the positive principal eigenvalue of an indefinite weighted problem, associated with the Neumann Laplacian in a box , which arise…
On a Cheeger--Kohler-Jobin inequality
Ilaria Lucardesi, Dario Mazzoleni, Berardo Ruffini
We discuss the minimization of a Kohler-Jobin type scale-invariant functional among open, convex, bounded sets, namely among open convex bounde…
Regularity of the free boundary for the vectorial Bernoulli problem
Dario Mazzoleni, Susanna Terracini, Bozhidar Velichkov
In this paper we study the regularity of the free boundary for a vector-valued Bernoulli problem, with no sign assumptions on the boundary data. More precisely, given an open, smoo…
Some estimates for the higher eigenvalues of sets close to the ball
Dario Mazzoleni, Aldo Pratelli
In this paper we investigate the behavior of the eigenvalues of the Dirichlet Laplacian on sets in whose first eigenvalue is close to the one of the ball with the sa…
Regularity of the optimal sets for some spectral functionals
Dario Mazzoleni, Susanna Terracini, Bozhidar Velichkov
In this paper we study the regularity of the optimal sets for the shape optimization problem \[ \min\Big\{λ_1(Ω)+\dots+λ_k(Ω)\ :\ Ω\subset\mathbb{R}^d,\ \text{open}\ ,\ |Ω|=1\Big\}…
Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets
Dario Mazzoleni, Davide Zucco
We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open sets of of fixed measure. We show that, by purely…
A surgery result for the spectrum of the Dirichlet Laplacian
Dorin Bucur, Dario Mazzoleni
In this paper we give a method to geometrically modify an open set such that the first eigenvalues of the Dirichlet Laplacian and its perimeter are not increasing, its measure…
Lipschitz regularity of the eigenfunctions on optimal domains
Dorin Bucur, Dario Mazzoleni, Aldo Pratelli +1
We study the optimal sets for spectral functionals , which are bi-Lipschitz with respect to each of the eigenvalues $λ_1…