Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

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

Ying Hu, Zhongmin Qian, and Zichen Zhang

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Abstract

In this paper, we establish several local and global gradient estimates for positive solutions of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques.

Résumé

Dans cet article, nous établissons plusieurs estimées (locales et globales) des gradients des solutions positives des équations aux milieux poreux et des équations de la diffusion rapide. Notre preuve est probabiliste et utilise des techniques de martingales.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 53, Number 4 (2017), 1793-1820.

Dates
Received: 10 April 2015
Revised: 1 June 2016
Accepted: 1 June 2016
First available in Project Euclid: 27 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1511773726

Digital Object Identifier
doi:10.1214/16-AIHP771

Mathematical Reviews number (MathSciNet)
MR3729635

Zentralblatt MATH identifier
06847062

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
Gradient estimate Porous medium equation Fast diffusion equation Martingale technique

Citation

Hu, Ying; Qian, Zhongmin; Zhang, Zichen. Gradient estimates for porous medium and fast diffusion equations by martingale method. Ann. Inst. H. Poincaré Probab. Statist. 53 (2017), no. 4, 1793--1820. doi:10.1214/16-AIHP771. https://projecteuclid.org/euclid.aihp/1511773726


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