20 citations · 118 across the 20 of their papers we have counts for
22 papers
Unweighted Hardy Inequalities on the Heisenberg Group and in Step-Two Carnot Groups
Lorenzo d'Arca, Luca Fanelli, Valentina Franceschi +1
We establish unweighted Hardy-type inequalities on step-two Carnot groups with one-dimensional vertical layer, with explicit lower bounds for the optimal Hardy constant. The approa…
Magnetic flows on 3D contact sub-Riemannian manifolds via the Rumin complex
Davide Barilari, Tania Bossio, Valentina Franceschi
We show that the appropriate notion of magnetic field on three-dimensional contact sub-Riemannian manifolds is given by a closed Rumin differential two-form. We introduce horizonta…
Embedded trace operator for infinite metric trees
Valentina Franceschi, Kiyan Naderi, Konstantin Pankrashkin
We consider a class of infinite weighted metric trees obtained as perturbations of self-similar regular trees. Possible definitions of the boundary traces of functions in the Sobol…
Mean value formulas on surfaces in Grushin spaces
Valentina Franceschi, Roberto Monti, Alessandro Socionovo
We prove (sub)mean value formulas at the point for (sub)harmonic functions a on a hypersurface where the differentiable structure and the surface…
The Cheeger problem in abstract measure spaces
Valentina Franceschi, Andrea Pinamonti, Giorgio Saracco +1
We consider non-negative -finite measure spaces coupled with a proper functional that plays the role of a perimeter. We introduce the Cheeger problem in this framework and e…
Local controllability does imply global controllability
Ugo Boscain, Daniele Cannarsa, Valentina Franceschi +1
We say that a control system is locally controllable if the attainable set from any state contains an open neighborhood of , while it is controllable if the attainable set f…
Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group
Biagio Cassano, Valentina Franceschi, David Krejcirik +1
In this paper we introduce a notion of magnetic field in the Heisenberg group and we study its influence on spectral properties of the corresponding magnetic (sub-elliptic) Laplaci…
On the Steiner property for planar minimizing clusters. The isotropic case
Valentina Franceschi, Aldo Pratelli, Giorgio Stefani
We consider the isoperimetric problem for clusters in the plane with a double density, that is, perimeter and volume depend on two weights. In this paper we consider the isotropic…
On the Steiner property for planar minimizing clusters. The anisotropic case
Valentina Franceschi, Aldo Pratelli, Giorgio Stefani
In this paper we discuss the Steiner property for minimal clusters in the plane with an anisotropic double density. This means that we consider the classical isoperimetric problem…
A cortical-inspired sub-Riemannian model for Poggendorff-type visual illusions
Emre Baspinar, Luca Calatroni, Valentina Franceschi +1
We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-i…
The isoperimetric problem for regular and crystalline norms in
Valentina Franceschi, Roberto Monti, Alberto Righini +1
We study the isoperimetric problem for anisotropic left-invariant perimeter measures on , endowed with the Heisenberg group structure. The perimeter is associated with…
Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling
Marcelo Bertalmío, Luca Calatroni, Valentina Franceschi +2
We consider the evolution model proposed in [9, 6] to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and d…
Visual illusions via neural dynamics: Wilson-Cowan-type models and the efficient representation principle
Marcelo Bertalmío, Luca Calatroni, Valentina Franceschi +3
In this work we have aimed to reproduce supra-threshold perception phenomena, specifically visual illusions, with Wilson-Cowan-type models of neuronal dynamics. We have found that…
Hardy-type inequalities for the Carnot-Carathéodory distance in the Heisenberg group
Valentina Franceschi, Dario Prandi
In this paper we study various Hardy inequalities in the Heisenberg group , w.r.t. the Carnot-Carathéodory distance from the origin. We firstly show that the optim…
Point interactions for 3D sub-Laplacians
Riccardo Adami, Ugo Boscain, Valentina Franceschi +1
In this paper we show that, for a sub-Laplacian on a -dimensional manifold , no point interaction centered at a point exists. When is complete w.r.t. the a…
A cortical-inspired model for orientation-dependent contrast perception: a link with Wilson-Cowan equations
Marcelo Bertalmío, Luca Calatroni, Valentina Franceschi +2
We consider a differential model describing neuro-physiological contrast perception phenomena induced by surrounding orientations. The mathematical formulation relies on a cortical…
Symmetric double bubbles in the Grushin plane
Valentina Franceschi, Giorgio Stefani
We address the double bubble problem for the anisotropic Grushin perimeter , , and the Lebesgue measure in , in the case of two equal volumes. We assume…
On the essential self-adjointness of singular sub-Laplacians
Valentina Franceschi, Dario Prandi, Luca Rizzi
We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. As a consequence, we sho…
CMC spheres in the Heisenberg group
Valentina Franceschi, Francescopaolo Montefalcone, Roberto Monti
We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group . These spheres are conjectured to be the isoperimetric sets of . We pr…
A minimal partition problem with trace constraint in the Grushin plane
Valentina Franceschi
We study a variational problem for the perimeter associated with the Grushin plane, called minimal partition problem with trace constraint. This consists in studying how to enclose…
Quantitative isoperimetric inequalities in H^n
Valentina Franceschi, Gian Paolo Leonardi, Roberto Monti
In the Heisenberg group H^n, we prove quantitative isoperimetric inequalities for Pansu's spheres, that are known to be isoperimetric under various assumptions. The inequalities ar…
Isoperimetric problem in H-type groups and Grushin spaces
Valentina Franceschi, Roberto Monti
We study the isoperimetric problem in H-type groups and Grushin spaces, emphasizing a relation between them. We prove existence, symmetry and regularity properties of isoperimetric…