The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916819781025792 |
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| author | Qin, Lei |
| author_facet | Qin, Lei |
| contents | In this paper, we prove that the first (positive) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator \[ L(u)=Δu-(\nabla u,x), \] is strongly log-concave if the domain is bounded and convex, which improves the conclusion in [6]. We also provide a characterization of the equality case of the Brunn-Minkowski inequality for the principal frequency of $L(u)$ in the class of convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00819 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies Qin, Lei Analysis of PDEs 52A20 In this paper, we prove that the first (positive) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator \[ L(u)=Δu-(\nabla u,x), \] is strongly log-concave if the domain is bounded and convex, which improves the conclusion in [6]. We also provide a characterization of the equality case of the Brunn-Minkowski inequality for the principal frequency of $L(u)$ in the class of convex bodies. |
| title | The strong log-concavity for first eigenfunction of the Ornstein-Uhlenbeck operator in the class of convex bodies |
| topic | Analysis of PDEs 52A20 |
| url | https://arxiv.org/abs/2507.00819 |