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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.07426 |
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| _version_ | 1866914343116865536 |
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| author | Colesanti, Andrea Qin, Lei Salani, Paolo |
| author_facet | Colesanti, Andrea Qin, Lei Salani, Paolo |
| contents | In this paper, we investigate the log-concavity of the kernel for the parabolic Ornstein-Uhlenbeck operator in a bounded, convex domain. Consequently, we get the preservation of the log-concavity of the initial datum by the related flow. As an application, we give another proof of a Brunn-Minkowski type inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and of the log-concavity of the related first eigenfunction (both results have been proved in [9], by different methods). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Log-concavity of solutions of parabolic equations related to the Ornstein-Uhlenbeck operator and applications Colesanti, Andrea Qin, Lei Salani, Paolo Analysis of PDEs In this paper, we investigate the log-concavity of the kernel for the parabolic Ornstein-Uhlenbeck operator in a bounded, convex domain. Consequently, we get the preservation of the log-concavity of the initial datum by the related flow. As an application, we give another proof of a Brunn-Minkowski type inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and of the log-concavity of the related first eigenfunction (both results have been proved in [9], by different methods). |
| title | Log-concavity of solutions of parabolic equations related to the Ornstein-Uhlenbeck operator and applications |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.07426 |