Fundamental Gaps for the Dirichlet \(p\)-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy

Rui Chen, Daniel Hauer

We study fundamental gaps for the Dirichlet \(p\)-Laplacian on bounded convex domains with convex potentials. We prove log-concavity of the positive first eigenfunction by a regula…