Gradient estimates for nonlinear diffusion semigroups by coupling methods

• 作者: Yongsheng Song
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（5）
• 所属期刊栏目: Articles
• 页码范围: 1093-1108
• 页数: 16页
• 语种: 英文

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.