Strong unique continuation for the Lamé system with Lipschitz coefficients
type: Item
instance of: scholarly article
title: Strong unique continuation for the Lamé system with Lipschitz coefficients
zbMATH Open document ID: 1082.35041
author: C.-L. Lin
author: Jenn-Nan Wang
published in: Mathematische Annalen
publication date: 2005-04-15T00:00:00Z
review text: The authors prove the strong unique continuation property (SUCP) for the equations of linear isotropic elasticity in \({\mathbb R}^2\). Extending previous results by \textit{G. Alexandrini} and \textit{A. Morassi} [Commun. Partial Differ. Equ. 26, 1787--1810 (2001; Zbl 1086.35016)], where a least \(C^{1,1}\)-coefficients must be assumed, they achieve (SUCP) in the case of Lipschitz coefficients. To this end they introduce a reduction to a first order system carefully avoiding differentiation of the coefficients. The resulting system has still some coupling in the principal part so (SUCP) cannot be inferred directly. Instead they give a two-step proof: Polynomial decay implies exponential decay which in turn implies vanishing in a neighbourhood.
reviewed by: Norbert Weck
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 74B05
zbMATH DE Number: 2156236
zbMATH Keywords: unique continuation
zbMATH Keywords: Lamè system
zbMATH Keywords: linear isotropic elasticity
zbMATH Keywords: coupling in the principal part
MaRDI profile type: Publication
full work available at URL: s00208-004-0597-z
OpenAlex ID: W2014017003
cites work: STRONG UNIQUE CONTINUATION FOR THE LAMÉ SYSTEM OF ELASTICITY1*
cites work: Q4386029
cites work: The unique continuation property of an elliptic system. The Lamé system
cites work: Q3834387
cites work: Unique continuation for elliptic operators: A geometric-variational approach
cites work: Q3139888
cites work: Q3736112
cites work: Uniqueness theorems for second order elliptic differential equations
cites work: The failure of rank-one connections
cites work: Strong unique continuation property for an elasticity system with residual stress
cites work: Unique Continuation for an Elasticity System with Residual Stress and Its Applications
cites work: Unique continuation for the two-dimensional anisotropic elasticity system and its applications to inverse problems
cites work: Strong unique continuation property for elliptic systems of normal type in two independent variables
cites work: Strong uniqueness for second order differential operators
cites work: Außenraumaufgaben in der Theorie stationärer Schwingungen inhomogener elastischer Körper
cites work: Unique continuation for systems with Lamé principal part
DOI: 10.1007/S00208-004-0597-Z
description: scientific article; zbMATH DE number 2156236