Degenerate Fokker-Planck Equations : Bismut Formula, Gradient Estimate and Harnack Inequality

2011/03/14 by Arnaud Guillin, Guillin, Arnaud, Feng‐Yu Wang +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Probability (math.PR)

paper · doi:10.48550/arxiv.1103.2817

openalex publication_date 2011/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By constructing successful couplings for degenerate diffusion processes, explicit derivative formula and Harnack type inequalities are presented for solutions to a class of degenerate Fokker-Planck equations on \R^m×\R^d. The main results are also applied to the study of gradient estimate, entropy/transportation-cost inequality and heat kernel inequalities.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

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