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

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 3, page 761-770
- ISSN: 1292-8119

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topYu, Hang. "Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 761-770. <http://eudml.org/doc/272755>.

@article{Yu2011,

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

author = {Yu, Hang},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Lamé system; Carleman estimate; strong unique continuation; polynomial weights},

language = {eng},

number = {3},

pages = {761-770},

publisher = {EDP-Sciences},

title = {Strong unique continuation for the Lamé system with Lipschitz coefficients in three dimensions},

url = {http://eudml.org/doc/272755},

volume = {17},

year = {2011},

}

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

PB - EDP-Sciences

VL - 17

IS - 3

SP - 761

EP - 770

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

LA - eng

KW - Lamé system; Carleman estimate; strong unique continuation; polynomial weights

UR - http://eudml.org/doc/272755

ER -

## References

top- [1] G. Alessandrini and A. Morassi, Strong unique continuation for the Lamé system of elasticity. Comm. P. D. E.26 (2001) 1787–1810. Zbl1086.35016MR1865945
- [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. Zbl0892.35054MR1608540
- [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. Zbl0832.73012MR1239100
- [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. Zbl1158.35353MR2215770
- [6] C.E. Kenig, J. Sjöstrand and G. Uhlmann, The Calderón problem with partial data. Ann. Math.165 (2007) 567–591. Zbl1127.35079MR2299741
- [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). Zbl1202.35325MR2730376
- [8] C.-L. Lin and J.-N. Wang, Strong unique continuation for the Lamé system with Lipschitz coefficients. Math. Ann.331 (2005) 611–629. Zbl1082.35041MR2122542
- [9] A. Martinez, An introduction to semiclassical and microlocal analysis. Springer-Verlag (2002). Zbl0994.35003MR1872698
- [10] R. Regbaoui, Strong uniqueness for second order differential operators J. Differ. Equ.141 (1997) 201–217. Zbl0887.35040MR1488350
- [11] M. Salo and L. Tzou, Carleman estimates and inverse problems for Dirac operators. Math. Ann.344 (2009) 161–184. Zbl1169.35063MR2481057
- [12] N. Weck, Außnraumaufgaben in der Theorie stationärer Schwingungen inhomogener elasticher Körper. Math. Z.111 (1969) 387–398. Zbl0176.09202MR263295
- [13] N. Weck, Unique continuation for systems with Lamé principal part. Math. Methods Appl. Sci.24 (2001) 595–605. Zbl0986.35117MR1834916
- [14] H. Yu, Three spheres inequalities and unique continuation for a three-dimensional Lamé system of elasticity with C1 coeffients. arXiv:0811.1262 (2008).

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