Gradient estimates for porous medium and fast diffusion equations via FBSDE approach

Ying Hu (1) , Zhongmin Qian (2) , Zichen Zhang (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MI - Mathematical Institute [Oxford]

In this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques and Forward and Backward Stochastic Differential Equations (FBSDEs).

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Ying Hu, Zhongmin Qian, Zichen Zhang. Gradient estimates for porous medium and fast diffusion equations via FBSDE approach. 2012. ⟨hal-00705097v1⟩