Heat kernels of second order complex elliptic operators and applications
type: Item
instance of: scholarly article
title: Heat kernels of second order complex elliptic operators and applications
zbMATH Open document ID: 0919.35035
author: Pascal Auscher
author: Philippe Tchamitchian
author: Alan McIntosh
published in: Journal of Functional Analysis
publication date: 1999-09-02T00:00:00Z
review text: The authors study second-order elliptic operators \({\mathcal L}\) on \(\mathbb{R}^n\) in divergence form: \[ {\mathcal L}=- \partial_{x_i}(a_{ij}(x) \partial_{x_j}- a_{i,n+1}(x))+ a_{n+1, j}\partial_{x_j}+ a_{n+1,n+1}(x), \] where the coefficients \(a_{ij}\), \(1\leq i, j\leq n+ 1\), are assumed complex-valued, bounded and, at least, measurable. When the space-dimension is larger than 3, the coefficients are assumed Hölder continuous and an ellipticity assumption is made. The authors are mainly interested in estimates for the (Green-) kernel of the resolvent and in heat-kernel estimates of Gaussian type. Estimates for operators are in Sobolev \(L^p\)-type spaces, and the authors also study square roots of the operators under consideration. In particular they study (and solve, making suitable assumptions) the ``Kato-square-root problem'', which consists in establishing the domain of the maximal accretive square-root of \({\mathcal L}\).
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 1121254
zbMATH Keywords: Kato-square-root problem
zbMATH Keywords: estimates for the kernel of the resolvent
zbMATH Keywords: heat-kernel estimates
reviewed by: Otto Liess
MaRDI profile type: Publication
OpenAlex ID: W2024814527
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DOI: 10.1006/JFAN.1997.3156
description: scientific article; zbMATH DE number 1121254