Uniformly elliptic operators with measurable coefficients
type: Item
instance of: scholarly article
title: Uniformly elliptic operators with measurable coefficients
zbMATH Open document ID: 0839.35034
published in: Journal of Functional Analysis
publication date: 1996-06-19T00:00:00Z
review text: The author considers higher-order elliptic operators \(H\), a typical example being \[ Hf= \Delta(a(x)\Delta f),\quad\text{with}\quad {1\over c}\leq a(x)\leq c,\;x\in \mathbb{R}^N,\text{ and } c> 0. \] He obtains pointwise upper bounds for the fundamental solution \(K(x, y, t)\) of the associated evolution equation \(df/dt= -Hf\). These bounds allow him to prove that the operators \(e^{- Ht}\) extend to strongly continuous holomorphic one-parameter semigroups on \(L^p\).
reviewed by: René Sperb
Mathematics Subject Classification ID: 35J30
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 35A08
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 790377
zbMATH Keywords: pointwise upper bounds for the fundamental solution
author: E. Brian Davies
MaRDI profile type: Publication
full work available at URL: jfan.1995.1103
OpenAlex ID: W2067187482
DOI: 10.1006/JFAN.1995.1103
description: scientific article; zbMATH DE number 790377