5 papers · 1 filter
Sharp Makai-type inequalities for the best Poincaré-Sobolev constants
Giovanni Pisante, Francesca Prinari
Given a bounded convex open set , we prove that the Poincaré-Sobolev constants can be bounded from below by the -power of the ratio betw…
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…
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…
On fractional Hardy-type inequalities in general open sets
Eleonora Cinti, Francesca Prinari
We show that, when , the sharp Hardy constant of the punctured space in the Sobolev-Slobodecki\uı space provides an optimal…