On the upper estimates of fundamental solutions of parabolic equations on Riemannian manifolds
type: Item
instance of: scholarly article
title: On the upper estimates of fundamental solutions of parabolic equations on Riemannian manifolds
zbMATH Open document ID: 0828.58030
author: Jiayu Li
author: Xin Shao
published in: Chinese Annals of Mathematics. Series B
publication date: 1996-01-08T00:00:00Z
review text: The authors consider the parabolic equation \[ \Delta u(x,t) + b(x,t) \nabla u(x,t) + h(x,t) u(x,t) - \partial u(x,t)/ \partial t = 0 \tag{1.1} \] on a complete Riemannian manifold \(M\). They derive the gradient estimates and Harnack inequalities for positive solutions of (1.1) and then derive the upper bounds of any positive \(L^2\) fundamental solution of (1.1) when \(h(x,t)\) and \(b(x,t)\) are indepenent of \(t\). Some generalizations of (1.1) are also under consideration. The methods developed earlier by the first author, P. Li and S. T. Yau are applied.
reviewed by: Yuri E. Gliklikh
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 58J60
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 743978
zbMATH Keywords: parabolic equation
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: gradient estimates
zbMATH Keywords: Harnack inequalities
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 743978