10 citations · 32 across the 13 of their papers we have counts for
15 papers
Three quantitative versions of the Pál inequality
Ilaria Lucardesi, Davide Zucco
The Pál inequality is a classical result which asserts that among all planar convex sets of given width the equilateral triangle is the one of minimal area. In this paper we prove…
Two extremum problems for Neumann eigenvalues
Lorenzo Cavallina, Kei Funano, Antoine Henrot +3
Neumann eigenvalues being non-decreasing with respect to domain inclusion, it makes sense to study the two shape optimization problems $\min\{μ_k(Ω):Ω\mbox{ convex},Ω\subset D, \}$…
About the Blaschke-Santalo diagram of area, perimeter and moment of inertia
Raphael Gastaldello, Antoine Henrot, Ilaria Lucardesi
We study the Blaschke-Santaló diagram associated to the area, the perimeter, and the moment of inertia. We work in dimension 2, under two assumptions on the shapes: convexity and t…
An isoperimetric problem with two distinct solutions
Antoine Henrot, Antoine Lemenant, Ilaria Lucardesi
In this paper we prove that among all convex domains of the plane with two axis of symmetry, the maximizer of the first non trivial Neumann eigenvalue with perimeter constrai…
A Blaschke-Lebesgue Theorem for the Cheeger constant
Antoine Henrot, Ilaria Lucardesi
In this paper we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine ana…
Body of constant width with minimal area in a given annulus
Antoine Henrot, Ilaria Lucardesi
In this paper we address the following shape optimization problem: find the planar domain of least area, among the sets with prescribed constant width and inradius. In the literatu…
On Blaschke-Santaló diagrams for the torsional rigidity and the first Dirichlet eigenvalue
Ilaria Lucardesi, Davide Zucco
We study Blaschke-Santaló diagrams associated to the torsional rigidity and the first eigenvalue of the Laplacian with Dirichlet boundary conditions. We work under convexity and vo…
Crack growth by vanishing viscosity in planar elasticity
Stefano Almi, Giuliano Lazzaroni, Ilaria Lucardesi
We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The cra…
Energy-dissipation balance of a smooth moving crack
Maicol Caponi, Ilaria Lucardesi, Emanuele Tasso
In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover…
Upscaling of screw dislocations with increasing tangential strain
Ilaria Lucardesi, Marco Morandotti, Riccardo Scala +1
The upscaling of a system of screw dislocations in a material subject to an external strain is studied. The -limit of a suitable rescaling of the renormalized energy is characte…
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…
Minimization of the eigenvalues of the dirichlet-laplacian with a diameter constraint
B Bogosel, A Henrot, I Lucardesi
In this paper we look for the domains minimizing the h-th eigenvalue of the Dirichlet-Laplacian h with a constraint on the diameter. Existence of an optimal domain is easily ob…
On two functionals involving the maximum of the torsion function
Antoine Henrot, Ilaria Lucardesi, Gérard Philippin
In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider and $M(Ω)λ_…
Confinement of dislocations inside a crystal with a prescribed external strain
Ilaria Lucardesi, Marco Morandotti, Riccardo Scala +1
A system of screw dislocations in an isotropic crystal undergoing antiplane shear is studied in the framework of linear elasticity. Imposing a suitable boundary condition for t…
A variational method for second order shape derivatives
Guy Bouchitté, Ilaria Fragalà, Ilaria Lucardesi
We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We…