Gradient estimates for porous medium and fast diffusion equations by martingale method

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 local and global gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques.

Mots clés: Gradient estimate; Porous medium equation; Fast diffusion equation; martingale technique

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 by martingale method. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2017, 53 (4), pp.1793-1820. ⟨10.1214/16-AIHP771⟩. ⟨hal-00705097v2⟩