11 citations · 29 across the 14 of their papers we have counts for
18 papers
An isoperimetric inequality for twisted eigenvalues with one orthogonality constraint
Emanuele Salato, Davide Zucco
We consider twisted eigenvalues , defined as the minimum of the Rayleigh quotient of functions in that are orthogonal to a given function $g\in L^2_\text…
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…
Ahlfors regularity of continua that minimize maxitive set functions
Davide Zucco
The primary objective of this paper is to establish the Ahlfors regularity of minimizers of set functions that satisfy a suitable maxitive condition on disjoint unions of sets. Our…
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…
Optimal partitioning of an interval and applications to Sturm-Liouville eigenvalues
Paolo Tilli, Davide Zucco
We study the optimal partitioning of a (possibly unbounded) interval of the real line into subintervals in order to minimize the maximum of certain set-functions, under rather…
Dirichlet conditions in Poincaré-Sobolev inequalities: the sub-homogeneous case
Davide Zucco
We investigate the dependence of optimal constants in Poincaré- Sobolev inequalities of planar domains on the region where the Dirichlet condition is imposed. More precisely, we lo…
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…
Strichartz Estimates for the Schrödinger Equation
Elena Cordero, Davide Zucco
The objective of this paper is to report on recent progress on Strichartz estimates for the Schrödinger equation and to present the state-of-the-art. These estimates have been obta…
Spectral partitions for Sturm-Liouville problems
Paolo Tilli, Davide Zucco
We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via Γ-convergence theory, we stu…
Transmission conditions obtained by homogenisation
Gianni Dal Maso, Giovanni Franzina, Davide Zucco
Given a bounded open set in , , and a sequence of compact sets converging to an -dimensional manifold , we study the asymptotic behaviour of…
Asymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length
Paolo Tilli, Davide Zucco
We consider the problem of maximizing the first eigenvalue of the -laplacian (possibly with non-constant coefficients) over a fixed domain , with Dirichlet conditions along $…
A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates
Elvise Berchio, Davide Buoso, Filippo Gazzola +1
We use a gap function in order to compare the torsional performances of different reinforced plates under the action of external forces. Then, we address a shape optimization probl…
Optimizing the first Dirichlet eigenvalue of the Laplacian with an obstacle
Antoine Henrot, Davide Zucco
Inside a fixed bounded domain of the plane, we look for the best compact connected set , of given perimeter, in order to maximize the first Dirichlet eigenvalue $λ_1(Ω\setmi…
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…
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…
Where best to place a Dirichlet condition in an anisotropic membrane?
Paolo Tilli, Davide Zucco
We study a shape optimization problem for the first eigenvalue of an elliptic operator in divergence form, with non constant coefficients, over a fixed domain . Dirichlet condit…
Strichartz Estimates for the Vibrating Plate Equation
Elena Cordero, Davide Zucco
We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schrödinger-type equations we show its close relation with the Schrödinger eq…
The Cauchy Problem for the Vibrating Plate Equation in modulation spaces
Elena Cordero, Davide Zucco
The local solvability of the Cauchy problem for the nonlinear vibrating plate equation is showed in the framework of modulation spaces. In the opposite direction, it is proved that…