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Steady States of Fokker–Planck Equations: III. Degenerate Diffusion

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Abstract

This is the third paper in a series concerning the study of steady states of a Fokker–Planck equation in a general domain in \({\mathbb R}^n\) with \(L^{p}_{loc}\) drift term and \(W^{1,p}_{loc}\) diffusion term for any \(p>n\). In this paper, we give some existence results of stationary measures of the Fokker–Planck equation under Lyapunov conditions which allow the degeneracy of diffusion.

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Acknowledgments

The first author was partially supported by NSFC Grants 11225105, 11431012. The second author was partially supported by NSFC Innovation Grant 10421101. The third author was partially supported by NSFC Grant 11271151 and the startup fund of Dalian University of Technology. The fourth author was partially supported by NSF Grants DMS0708331 and DMS1109201, NSERC discovery Grant 1257749, a faculty development Grant from University of Alberta, and a Scholarship from Jilin University.

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Wen Huang

  2. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, People’s Republic of China

    Wen Huang

  3. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China

    Min Ji

  4. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Zhenxin Liu

  5. Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Yingfei Yi

  6. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Zhenxin Liu & Yingfei Yi

  7. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Yingfei Yi

Authors
  1. Wen Huang
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  2. Min Ji
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  3. Zhenxin Liu
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  4. Yingfei Yi
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Correspondence to Min Ji.

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Huang, W., Ji, M., Liu, Z. et al. Steady States of Fokker–Planck Equations: III. Degenerate Diffusion. J Dyn Diff Equat 28, 127–141 (2016). https://doi.org/10.1007/s10884-015-9476-4

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  • DOI: https://doi.org/10.1007/s10884-015-9476-4

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