Gradient estimates for nonlinear diffusion semigroups by coupling methods  

作　　者：Yongsheng Song 

机构地区：[1]RCSDS,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China Mathematics》2021年第5期1093-1108,共16页中国科学：数学（英文版）

基　　金：supported by NCMIS, National Natural Science Foundation of China (Grant Nos.11871458 and 11688101);Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No.QYZDB-SSW-SYS017)。

摘　　要：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.

关 键 词：gradient estimates coupling methods G-EXPECTATION nonlinear PDEs 

分 类 号：O152.7[理学—数学]