Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 761-770.

This paper studies the strong unique continuation property for the Lamé system of elasticity with variable Lamé coefficients λ, µ in three dimensions, div (μ(∇u+∇u t ))+∇(λ 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.

DOI : 10.1051/cocv/2010021
Classification : 35B60, 74B05
Mots-clés : Lamé system, Carleman estimate, strong unique continuation 
@article{COCV_2011__17_3_761_0,
     author = {Yu, Hang},
     title = {Strong unique continuation for the {Lam\'e} system with {Lipschitz} coefficients in three dimensions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {761--770},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {3},
     year = {2011},
     doi = {10.1051/cocv/2010021},
     mrnumber = {2826979},
     zbl = {1227.35109},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2010021/}
}
TY  - JOUR
AU  - Yu, Hang
TI  - Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2011
SP  - 761
EP  - 770
VL  - 17
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/cocv/2010021/
DO  - 10.1051/cocv/2010021
LA  - en
ID  - COCV_2011__17_3_761_0
ER  - 
%0 Journal Article
%A Yu, Hang
%T Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2011
%P 761-770
%V 17
%N 3
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/cocv/2010021/
%R 10.1051/cocv/2010021
%G en
%F COCV_2011__17_3_761_0
Yu, Hang. Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 761-770. doi : 10.1051/cocv/2010021. http://www.numdam.org/articles/10.1051/cocv/2010021/

[1] G. Alessandrini and A. Morassi, Strong unique continuation for the Lamé system of elasticity. Comm. P. D. E. 26 (2001) 1787-1810. | MR | Zbl

[2] D.D. Ang, M. Ikehata, D.D. Trong and M. Yamamoto, Unique continuation for a stationary isotropic Lamé system with varaiable coefficients. Comm. P. D. E. 23 (1998) 371-385. | MR | Zbl

[3] B. Dehman and L. Robbiano, La propriété du prolongement unique pour un système elliptique : le système de Lamé. J. Math. Pures Appl. 72 (1993) 475-492. | MR | Zbl

[4] M. Eller, Carleman estimates for some elliptic systems. J. Phys. Conference Series 124 (2008) 012023.

[5] L. Escauriaza, Unique continuation for the system of elasticity in the plan. Proc. Amer. Math. Soc. 134 (2005) 2015-2018. | MR | Zbl

[6] C.E. Kenig, J. Sjöstrand and G. Uhlmann, The Calderón problem with partial data. Ann. Math. 165 (2007) 567-591. | MR | Zbl

[7] C.-L. Lin, G. Nakamura and J.-N. Wang, Optimal three-ball inequalities and quantitative uniqueness for the Lamé system with Lipschitz coefficients. arXiv:0901.4638 (2009). | MR | Zbl

[8] C.-L. Lin and J.-N. Wang, Strong unique continuation for the Lamé system with Lipschitz coefficients. Math. Ann. 331 (2005) 611-629. | MR | Zbl

[9] A. Martinez, An introduction to semiclassical and microlocal analysis. Springer-Verlag (2002). | MR | Zbl

[10] R. Regbaoui, Strong uniqueness for second order differential operators J. Differ. Equ. 141 (1997) 201-217. | MR | Zbl

[11] M. Salo and L. Tzou, Carleman estimates and inverse problems for Dirac operators. Math. Ann. 344 (2009) 161-184. | MR | Zbl

[12] N. Weck, Außnraumaufgaben in der Theorie stationärer Schwingungen inhomogener elasticher Körper. Math. Z. 111 (1969) 387-398. | MR | Zbl

[13] N. Weck, Unique continuation for systems with Lamé principal part. Math. Methods Appl. Sci. 24 (2001) 595-605. | MR | Zbl

[14] H. Yu, Three spheres inequalities and unique continuation for a three-dimensional Lamé system of elasticity with C1 coeffients. arXiv:0811.1262 (2008).

Cité par Sources :