On Gaussian interpolation inequalities
This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincaré and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo–Nirenberg–Sobolev inequalities on spheres. Entropy methods are investigated using not only...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-02-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.488/ |
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| author | Brigati, Giovanni Dolbeault, Jean Simonov, Nikita |
| author_facet | Brigati, Giovanni Dolbeault, Jean Simonov, Nikita |
| author_sort | Brigati, Giovanni |
| collection | DOAJ |
| description | This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincaré and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo–Nirenberg–Sobolev inequalities on spheres. Entropy methods are investigated using not only heat flow techniques but also nonlinear diffusion equations as on spheres. A new stability result is established for the Gaussian measure, which is directly inspired by recent results for spheres. |
| format | Article |
| id | doaj-art-8bed2de163284c1792c393bcd6b0fd98 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-8bed2de163284c1792c393bcd6b0fd982025-02-07T11:12:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-02-01362G1214410.5802/crmath.48810.5802/crmath.488On Gaussian interpolation inequalitiesBrigati, Giovanni0https://orcid.org/0000-0002-3698-9995Dolbeault, Jean1https://orcid.org/0000-0003-4234-2298Simonov, Nikita2https://orcid.org/0000-0002-3241-190XCEREMADE (CNRS UMR n ∘ 7534), PSL University, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775 Paris 16, FranceCEREMADE (CNRS UMR n ∘ 7534), PSL University, Université Paris-Dauphine, Place de Lattre de Tassigny, 75775 Paris 16, FranceLJLL (CNRS UMR n ∘ 7598) Sorbonne Université, 4 place Jussieu, 75005 Paris, FranceThis paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincaré and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo–Nirenberg–Sobolev inequalities on spheres. Entropy methods are investigated using not only heat flow techniques but also nonlinear diffusion equations as on spheres. A new stability result is established for the Gaussian measure, which is directly inspired by recent results for spheres.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.488/logarithmic Sobolev inequalityGagliardo–Nirenberg–Sobolev inequalitiesGaussian Poincaré inequalityspherespectral decompositionentropy methodsOrnstein–Uhlenbeck operatornonlinear diffusionsimproved inequalitiesstability |
| spellingShingle | Brigati, Giovanni Dolbeault, Jean Simonov, Nikita On Gaussian interpolation inequalities Comptes Rendus. Mathématique logarithmic Sobolev inequality Gagliardo–Nirenberg–Sobolev inequalities Gaussian Poincaré inequality sphere spectral decomposition entropy methods Ornstein–Uhlenbeck operator nonlinear diffusions improved inequalities stability |
| title | On Gaussian interpolation inequalities |
| title_full | On Gaussian interpolation inequalities |
| title_fullStr | On Gaussian interpolation inequalities |
| title_full_unstemmed | On Gaussian interpolation inequalities |
| title_short | On Gaussian interpolation inequalities |
| title_sort | on gaussian interpolation inequalities |
| topic | logarithmic Sobolev inequality Gagliardo–Nirenberg–Sobolev inequalities Gaussian Poincaré inequality sphere spectral decomposition entropy methods Ornstein–Uhlenbeck operator nonlinear diffusions improved inequalities stability |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.488/ |
| work_keys_str_mv | AT brigatigiovanni ongaussianinterpolationinequalities AT dolbeaultjean ongaussianinterpolationinequalities AT simonovnikita ongaussianinterpolationinequalities |