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The Dual Hamilton–Jacobi Equation and the Poincaré Inequality

Author

Listed:
  • Rigao He

    (Department of Mathematics, Jiangxi University of Science and Technology, Ganzhou 341000, China)

  • Wei Wang

    (School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Jianglin Fang

    (College of Science, Hunan Institute of Engineering, Xiangtan 411104, China)

  • Yuanlin Li

    (Department of Mathematics, Jiangxi University of Science and Technology, Ganzhou 341000, China)

Abstract

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.

Suggested Citation

  • Rigao He & Wei Wang & Jianglin Fang & Yuanlin Li, 2024. "The Dual Hamilton–Jacobi Equation and the Poincaré Inequality," Mathematics, MDPI, vol. 12(24), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3927-:d:1543117
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