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Variational Approximation for Fokker–Planck Equation on Riemannian Manifold
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  • Published: 19 April 2006

Variational Approximation for Fokker–Planck Equation on Riemannian Manifold

  • Xicheng Zhang1 

Probability Theory and Related Fields volume 137, pages 519–539 (2007)Cite this article

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Abstract

Under the bounded geometry assumption on Riemannian manifold M, a variational approximation for Fokker–Planck equation on M is constructed by the scheme of Jordan et al. in SIAM J Math Anal 29(1):1–17, 1998. Moreover, the uniqueness and global L p-estimate of the solution for 1 < p < dim(M)/(dim(M) − 1) are obtained for a broad class of potential.

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Authors and Affiliations

  1. Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, P.R. China

    Xicheng Zhang

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  1. Xicheng Zhang
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Correspondence to Xicheng Zhang.

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Cite this article

Zhang, X. Variational Approximation for Fokker–Planck Equation on Riemannian Manifold. Probab. Theory Relat. Fields 137, 519–539 (2007). https://doi.org/10.1007/s00440-006-0001-x

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  • Received: 17 April 2005

  • Revised: 14 February 2006

  • Published: 19 April 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0001-x

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AMS Subject Classifications

  • 35A15
  • 35K15
  • 58J35
  • 60A10
  • 60J60

Keywords

  • Fokker–Planck equation
  • Wasserstein metric
  • Gradient flow
  • Free energy
  • Heat kernel
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