The paper proves log-concavity of the first p-eigenfunction with convex potentials, a sharp one-dimensional gap inequality for every p>1, and a higher-dimensional p=2 collapse dichotomy.
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Fundamental Gaps for the Dirichlet \(p\)-Laplacian with Convex Potentials: Sharp One-Dimensional Bounds and a Higher-Dimensional Dichotomy
The paper proves log-concavity of the first p-eigenfunction with convex potentials, a sharp one-dimensional gap inequality for every p>1, and a higher-dimensional p=2 collapse dichotomy.