6 papers
Low eigenvalues of the Laplacian in general open sets
Lorenzo Brasco, Luca Briani, Francesca Prinari
We consider the minmax Ljusternik-Schnirelmann levels of the constrained Dirichlet integral, on a general open set of the Euclidean space. We show that, whenever one of these l…
Extremals for sharp Poincaré-Sobolev inequalities: periodically perforated sets and beyond
Lorenzo Brasco, Luca Briani, Francesca Prinari
We consider periodically perforated unbounded open sets and prove existence of extremals for the relevant sharp Poincaré-Sobolev embedding constant. The existence result holds no…
A Schrödinger operator with confining potential having quadratic growth
Chiara Alessi, Lorenzo Brasco, Michele Miranda
We study the spectral properties of a Schrödinger operator, in presence of a confining potential given by the distance squared from a fixed compact potential well. We prove contin…
Extremals for Poincaré-Sobolev sharp constants in Steiner symmetric sets
Lorenzo Brasco, Luca Briani, Francesca Prinari
We prove existence of minimizers for the sharp Poincaré-Sobolev constant in general Steiner symmetric sets, in the subcritical and superhomogeneous regime. The sets considered are…
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 Shu…