6 papers
A geometric lower bound for the clamped plate eigenvalue problem in low dimensions and extensions
Francesca Bianchi, Francesco Bozzola, Lorenzo Brasco
We show that the spectrum of the Dirichlet-biLaplacian can be quantitatively bounded from below in terms of the inradius only, for a general open set in dimensions and . For…
Equilibria of aggregation-diffusion models with nonlinear potentials
Francesco Bozzola, Edoardo Mainini
We consider an evolution model with nonlinear diffusion of porous medium type in competition with a nonlocal drift term favoring mass aggregation. The distinguishing trait of the m…
Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities
Francesco Bozzola, Matteo Talluri
We prove estimates for the sharp constants in fractional Poincaré-Sobolev inequalities associated to an open set, in terms of a nonlocal capacitary extension of its inradius. This…
Variations on the capacitary inradius
Francesco Bozzola, Lorenzo Brasco
We discuss some properties of the capacitary inradius for an open set. This is an extension of the classical concept of inradius (i.e. the radius of a largest inscribed ball), whic…
Capacitary inradius and Poincaré-Sobolev inequalities
Francesco Bozzola, Lorenzo Brasco
We prove a two-sided estimate on the sharp Poincaré constant of a general open set, in terms of a capacitary variant of its inradius. This extends a result by Maz'ya and Shub…
The role of topology and capacity in some bounds for principal frequencies
Francesco Bozzola, Lorenzo Brasco
We prove a lower bound on the sharp Poincaré-Sobolev embedding constants for general open sets, in terms of their inradius. We consider the following two situations: planar sets wi…