ESAIM: Control, Optimisation and Calculus of Variations

Table of Contents - July 2011 - Volume 17, Issue 03  

Research Article

Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions*

Yu, Hang

School of Mathematical Sciences, Fudan University, 200433 Shanghai, P.R. China. hangyumath@hotmail.com

Abstract

This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µ in three dimensions, ${\rm{div}}(\mu(\nabla u+\nabla u^t))+ \nabla(\lambda{\rm{div}} u)+Vu=0$ where λ and μ are Lipschitz continuous and V ∈ L∞. The method is based on the Carleman estimate with polynomial weights for the Lamé operator.

(Received September 24 2009)

(Revised January 25 2010)

(Online publication April 23 2010)

Key Words:

  • Lamé system;
  • Carleman estimate;
  • strong unique continuation

Mathematics Subject Classification:

  • 35B60;
  • 74B05

Footnotes

*  The author was supported in part by NSFC (No. 10801041 and 10831007), FANEDD (No. 200522) and NCET (No. 06-0359).