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math.AP2026
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 between…
math.AP2026
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…