Gaussian upper bounds on heat kernels of uniformly elliptic operators on bounded domains
type: Item
instance of: scholarly article
zbMATH Open document ID: 1265.35127
author: Narinder S. Claire
publication date: 2012-10-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0212068
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35K08
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 6090234
zbMATH Keywords: heat kernel
zbMATH Keywords: parabolic
zbMATH Keywords: uniformly elliptic
zbMATH Keywords: gaussian bounds
MaRDI profile type: Publication
arXiv ID: math/0212068
title: Gaussian upper bounds on heat kernels of uniformly elliptic operators on bounded domains
published in: Journal of Operator Theory
review text: The author obtains Gaussian upper bounds for heat kernels of higher order differential operators NEWLINE\[NEWLINEHf(x)=\sum_{|\alpha|\leq m,|\beta|\leq m}(-1)^{|\alpha|}D^\alpha (a_{\alpha,\beta}(x)D^\beta f(x))NEWLINE\]NEWLINE with Dirichlet boundary conditions on bounded domains in \(\mathbb R^N\). The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close to the boundary as well as the long-time exponential decay implied by the spectral gap. The coefficients of the operator supposed to be only bounded and measurable.
reviewed by: Lubomira Softova
description: scientific article; zbMATH DE number 6090234