The Dual Hamilton–Jacobi Equation and the Poincaré Inequality
Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic Sobolev inequalities and the hypercontractivit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/24/3927 |
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| author | Rigao He Wei Wang Jianglin Fang Yuanlin Li |
| author_facet | Rigao He Wei Wang Jianglin Fang Yuanlin Li |
| author_sort | Rigao He |
| collection | DOAJ |
| description | Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic Sobolev inequalities and the hypercontractivity of solutions of dual Hamilton–Jacobi equations. In addition, Poincaré inequality is also recovered by the dual Hamilton–Jacobi equations. |
| format | Article |
| id | doaj-art-f256d6fd13a94d9abd0265d8bb03f5b9 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-f256d6fd13a94d9abd0265d8bb03f5b92024-12-27T14:38:02ZengMDPI AGMathematics2227-73902024-12-011224392710.3390/math12243927The Dual Hamilton–Jacobi Equation and the Poincaré InequalityRigao He0Wei Wang1Jianglin Fang2Yuanlin Li3Department of Mathematics, Jiangxi University of Science and Technology, Ganzhou 341000, ChinaSchool of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, ChinaCollege of Science, Hunan Institute of Engineering, Xiangtan 411104, ChinaDepartment of Mathematics, Jiangxi University of Science and Technology, Ganzhou 341000, ChinaFollowing the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic Sobolev inequalities and the hypercontractivity of solutions of dual Hamilton–Jacobi equations. In addition, Poincaré inequality is also recovered by the dual Hamilton–Jacobi equations.https://www.mdpi.com/2227-7390/12/24/3927the logarithmic Sobolev inequalityHamilton–Jacobi equationthe Prékopa–Leindler inequalityPoincaré inequalitythe Brunn–Minkowski inequality |
| spellingShingle | Rigao He Wei Wang Jianglin Fang Yuanlin Li The Dual Hamilton–Jacobi Equation and the Poincaré Inequality Mathematics the logarithmic Sobolev inequality Hamilton–Jacobi equation the Prékopa–Leindler inequality Poincaré inequality the Brunn–Minkowski inequality |
| title | The Dual Hamilton–Jacobi Equation and the Poincaré Inequality |
| title_full | The Dual Hamilton–Jacobi Equation and the Poincaré Inequality |
| title_fullStr | The Dual Hamilton–Jacobi Equation and the Poincaré Inequality |
| title_full_unstemmed | The Dual Hamilton–Jacobi Equation and the Poincaré Inequality |
| title_short | The Dual Hamilton–Jacobi Equation and the Poincaré Inequality |
| title_sort | dual hamilton jacobi equation and the poincare inequality |
| topic | the logarithmic Sobolev inequality Hamilton–Jacobi equation the Prékopa–Leindler inequality Poincaré inequality the Brunn–Minkowski inequality |
| url | https://www.mdpi.com/2227-7390/12/24/3927 |
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