On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. I
type: Item
instance of: scholarly article
title: On the \(L_{p}\)-theory of \(C_{0}\)-semigroups associated with second-order elliptic operators. I
zbMATH Open document ID: 1020.47028
author: Zeev Sobol
author: Hendrik Vogt
published in: Journal of Functional Analysis
publication date: 2002-11-28T00:00:00Z
review text: The authors study the \(L_p\) properties of second-order elliptic differential operators corresponding to expressions \(\Lambda=-\nabla. (a\nabla)+ b.\nabla+ \nabla.c+V\) with singular measurable coefficients \(a,b,c,V\). They use the associated sesquilinear form \(\tau\) and give a general method of constructing positive \(C_0\)-semigroups on \(L_p\) corresponding to a not necessarily sectorial form \(t\) on \(L_2\). Their approach is based upon approximations by sectorial forms where the potential is approximated. The procedure is realized by the use of the perturbation theory of positive operators. [For Part II, see the following review)].
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D09
zbMATH DE Number: 1836671
zbMATH Keywords: \(L_p\) properties of second-order elliptic differential operators
zbMATH Keywords: positive \(C_0\)-semigroups
zbMATH Keywords: approximations by sectorial forms
zbMATH Keywords: perturbation theory of positive operators
reviewed by: Miklavž Mastinšek
MaRDI profile type: Publication
full work available at URL: jfan.2001.3908
OpenAlex ID: W2010568808
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DOI: 10.1006/JFAN.2001.3908
description: scientific article; zbMATH DE number 1836671