Regularized Brascamp-Lieb inequalities via Optimal Transport and Study of Equality Cases

Fuente: arXiv
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Main Author: Ammari, Bader
Format: Preprint
Published: 2026
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_version_ 1866918493359702016
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