Estimates of Dirichlet heat kernels
type: Item
instance of: scholarly article
title: Estimates of Dirichlet heat kernels
zbMATH Open document ID: 0933.58027
DOI: 10.1016/S0304-4149(97)00108-7
author: Feng-Yu Wang
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: Let \(M\) be a connected Riemannian manifold and \(D\subset M\) a bounded open regular domain. Denote by \(p^D_t(x,y)\) the Dirichlet heat kernel, that is, the fundamental solution of the heat equation \[ \partial_t u(t,x)=Lu(t,x),\quad u|_{\partial D}=0 \] on \(D\) where \(L=\frac {1}{2}(\Delta +Z)\), \(Z\) being a smooth vector field. Explicit lower bounds on \(p^D_t\) and two-side comparison results are obtained by means of logarithmic transformations that allows to derive a Bismut type derivative formula. The Li-Yau type Harnack inequality is also established.
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 58J65
zbMATH DE Number: 1364466
zbMATH Keywords: Dirichlet heat kernel
zbMATH Keywords: diffusion process
zbMATH Keywords: Harnack inequality
MaRDI profile type: Publication
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full work available at URL: s0304-4149(97)00108-7
OpenAlex ID: W1490022507
description: scientific article; zbMATH DE number 1364466