6 papers
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…
Stochastic homogenization of nonconvex unbounded integral functionals with generalized Orlicz growth
Davide Aruta, Francesca Prinari, Francesco Solombrino
We consider the homogenization of random integral functionals which are possibly unbounded, that is, the domain of the integrand is not the whole space and may depend on the space-…
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…