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

2012/06/07 by Ying Hu, Zhongmin Qian, Hu, Ying +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR) #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.1206.1394

openalex publication_date 2012/06/07 · arxiv created 2015/05/21 · arxiv updated 2015/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the parabolic kernel of the Schrödinger operator

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