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Gradient estimates for nonlinear diffusion semigroups by coupling methods

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Abstract

In this paper, we obtain gradient estimates for certain nonlinear partial differential equations by coupling methods. First, we derive uniform gradient estimates for certain semi-linear PDEs based on the coupling method introduced by Wang in 2011 and the theory of backward SDEs. Then we generalize Wang's coupling to the G-expectation space and obtain gradient estimates for nonlinear diffusion semigroups, which correspond to the solutions of certain fully nonlinear PDEs.

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Acknowledgements

This work was supported by NCMIS, National Natural Science Foundation of China (Grant Nos. 11871458 and 11688101) and Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDB-SSW-SYS017).

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Authors and Affiliations

  1. RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yongsheng Song

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yongsheng Song

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  1. Yongsheng Song
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Correspondence to Yongsheng Song.

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Song, Y. Gradient estimates for nonlinear diffusion semigroups by coupling methods. Sci. China Math. 64, 1093–1108 (2021). https://doi.org/10.1007/s11425-018-9541-6

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  • DOI: https://doi.org/10.1007/s11425-018-9541-6

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