Sharp Makai-type inequalities for the best Poincaré-Sobolev constants

Giovanni Pisante, Francesca Prinari

Given a bounded convex open set $\Omega \subseteq {\mathbb{R}}^N$, we prove that the Poincaré-Sobolev constants ${\lambda }_{p,q}(\Omega )$ can be bounded from below by the $p$-power of the ratio between…