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 hypercontractivity of solutions of dual Hamilton–Jacobi equations. In addition, Poincaré inequality is also recovered by the dual Hamilton–Jacobi equations.
Authors
- Yuanlin Li (ORCID: https://orcid.org/0000-0001-5466-6164)
- Rigao He (ORCID: https://orcid.org/0000-0001-7811-329X)
- Wei Wang (ORCID: https://orcid.org/0000-0001-9170-8271)
- Jianglin Fang (ORCID: https://orcid.org/0000-0002-7920-0966)
Institutions
- Hunan University of Science and Technology (CN)
- Hunan Institute of Engineering (CN)
- Jiangxi University of Science and Technology (CN)
Publication Details
- Journal
- Mathematics
- Published
- 2024-12-13
- DOI
- https://doi.org/10.3390/math12243927
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- Natural Science Foundation of Jiangxi Province
- Natural Science Foundation of Hunan Province
- Education Department of Jiangxi Province
- Scientific Research Foundation of Hunan Provincial Education Department