A sharp quantitative nonlinear Poincaré inequality on convex domains

Vincenzo Amato, Dorin Bucur, Ilaria Fragalà

For any $p\in (1,+\infty )$, we give a new inequality for the first nontrivial Neumann eigenvalue ${\mu }_p(\Omega ,\phi )$ of the $p$-Laplacian on a convex domain $\Omega \subset {\mathbb{R}}^N$ wi…