20 citations · 118 across the 20 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
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…