Gradient estimates of Poisson equations on Riemannian manifolds and applications
type: Item
instance of: scholarly article
title: Gradient estimates of Poisson equations on Riemannian manifolds and applications
zbMATH Open document ID: 1181.58015
published in: Journal of Functional Analysis
publication date: 2009-12-18T00:00:00Z
review text: Let \(\mathcal L\) be the reflected diffusion generated by \(\Delta -\nabla V \cdot \nabla\) over a connected and complete Riemannian manifold \(M\) with empty or convex boundary. The author establishes some sharp estimates for \(\sup_{x\in M}|\nabla G|(x)\) in terms of the dimension, the diameter and the lower bound of curvature, where \(\mathcal G\) is the solution to the Poisson equation \(-\mathcal LG=g.\) Applications are given to the transportation-information inequality, to Cheeger's isoperimetric inequality and to the Gaussian concentration inequality.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 5649986
zbMATH Keywords: Poisson equations
zbMATH Keywords: gradient estimates
zbMATH Keywords: transportation inequalities
zbMATH Keywords: isoperimetric inequalities
author: Liming Wu
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.07.013
OpenAlex ID: W2079296312
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DOI: 10.1016/J.JFA.2009.07.013
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description: scientific article; zbMATH DE number 5649986