Regularized Brascamp-Lieb inequalities via Optimal Transport and Study of Equality Cases
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918493359702016 |
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| author | Ammari, Bader |
| author_facet | Ammari, Bader |
| contents | We consider regularized Brascamp-Lieb inequalities using the theory of optimal transportation, more precisely an anisotropic version of Caffarelli's contraction theorem. Furthermore, we provide a full picture concerning the issues of finiteness of the Brascamp-Lieb constant and of the existence of Gaussian extremizers. We also find all optimizers for these regularized Brascamp-Lieb inequalities by employing heat flow methods that were already used to settle this question for the non-regularized Brascamp-Lieb inequality and introducing new ideas to deal with several difficulties, which do not appear for the non-regularized Brascamp-Lieb datum. Finally, we give some interesting applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21267 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularized Brascamp-Lieb inequalities via Optimal Transport and Study of Equality Cases Ammari, Bader Analysis of PDEs Functional Analysis 26D15, 52A40, 49Q20, 35K05 We consider regularized Brascamp-Lieb inequalities using the theory of optimal transportation, more precisely an anisotropic version of Caffarelli's contraction theorem. Furthermore, we provide a full picture concerning the issues of finiteness of the Brascamp-Lieb constant and of the existence of Gaussian extremizers. We also find all optimizers for these regularized Brascamp-Lieb inequalities by employing heat flow methods that were already used to settle this question for the non-regularized Brascamp-Lieb inequality and introducing new ideas to deal with several difficulties, which do not appear for the non-regularized Brascamp-Lieb datum. Finally, we give some interesting applications. |
| title | Regularized Brascamp-Lieb inequalities via Optimal Transport and Study of Equality Cases |
| topic | Analysis of PDEs Functional Analysis 26D15, 52A40, 49Q20, 35K05 |
| url | https://arxiv.org/abs/2603.21267 |