Year: 2026
Type: preprint
Abstract: Let $u$ be the first Dirichlet Laplacian eigenfunction of a bounded convex set $Ω$ in $\mathbb{R}^n$. We strengthen the classical result by Brascamp-Lieb which asserts that $u$ is logconcave in $Ω$: we prove that, if $u$ is normalized so that its $L^\infty$-norm does not exceed a threshold $\overlineκ (Ω)<1$ depending explicitly on the diameter of the domain and on its principal frequency, the function $- ( - \log u ) ^{1/2}$ is concave in $Ω$.
Source: arXiv (Cornell University)
Authors: Crasta, Graziano, Fragalà, Ilaria
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7133259115
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