Power-logconcavity of the Laplacian ground state
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912930943991808 |
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| author | Crasta, Graziano Fragalà, Ilaria |
| author_facet | Crasta, Graziano Fragalà, Ilaria |
| contents | 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 $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24093 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Power-logconcavity of the Laplacian ground state Crasta, Graziano Fragalà, Ilaria Analysis of PDEs 35E10, 35J25, 35K05, 26B25 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 $Ω$. |
| title | Power-logconcavity of the Laplacian ground state |
| topic | Analysis of PDEs 35E10, 35J25, 35K05, 26B25 |
| url | https://arxiv.org/abs/2602.24093 |