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Mathematische Annalen

, Volume 331, Issue 3, pp 611–629 | Cite as

Strong unique continuation for the Lamé system with Lipschitz coefficients

  • Ching-Lung Lin
  • Jenn-Nan WangEmail author
Article

Abstract.

In this paper we prove the strong unique continuation property for a Lamé system with Lipschitz coefficients in the plane. The proof relies on reducing the Lamé system to a first order elliptic system and suitable Carleman estimates with polynomial weights.

Keywords

Elliptic System Unique Continuation Carleman Estimate Polynomial Weight Unique Continuation Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alessandrini, G., Morassi, A.: Strong unique continuation for the Lamé system of elasticity. Comm. in. PDE. 26, 1787–1810 (2001)zbMATHGoogle Scholar
  2. 2.
    Ang, D.D., Ikehata, M., Trong, D.D., Yamamoto, M.: Unique continuation for a stationary isotropic Lamé system with varaiable coefficients. Comm. in. PDE 23, 371–385 (1998)zbMATHGoogle Scholar
  3. 3.
    Dehman, B., Robbiano, L.: La propriété du prolongement unique pour un système elliptique: le système Lamé. J. Math. Pures Appl. 72, 475–492 (1993)zbMATHGoogle Scholar
  4. 4.
    Garofalo, N., Lin, F.H.: Monotonicity properties of variational integrals, Ap weights and unique continuation. Indiana Univ. Math. J. 35, 245–268 (1986)zbMATHGoogle Scholar
  5. 5.
    Garofalo, N., Lin, F.H.: Unique continuation for elliptic operators: a geometric-variational approach. Comm. in. Pure Appl. Math. 40, 347–366 (1987)zbMATHGoogle Scholar
  6. 6.
    Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems. Birkhäuser Verlag, 1993Google Scholar
  7. 7.
    Hörmander, L.: The Analysis of Linear Partial Differential Operators. Vol. III, Springer-Verlag, Berlin/New York, 1985Google Scholar
  8. 8.
    Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. in. PDE. 8(1), 21–64 (1983)Google Scholar
  9. 9.
    Iwaniec, T., Verchota, G., Vogel, A.: The failure of rank-one connections. Arch. Ration. Mech. Anal. 163, 125–169 (2002)CrossRefzbMATHGoogle Scholar
  10. 10.
    Lin, C.-L.: Strong unique continuation for an elasticity system with residual stress. Indiana Univ. Math. J. In pressGoogle Scholar
  11. 11.
    Nakamura, G., Wang, J.-N.: Unique continuation for an elasticity system with residual stress and its applications. SIAM J. Math. Anal. 35, 304–317 (2003)zbMATHGoogle Scholar
  12. 12.
    Nakamura, G., Wang, J.N.: Unique continuation for the two-dimensional anisotropic elasticity system and its application to inverse problems. SubmittedGoogle Scholar
  13. 13.
    Open image in new window, T.: Strong unique continuation property for elliptic systems of normal type in two independent variables. Tohoku Math. J. 54, 309–318 (2002)Google Scholar
  14. 14.
    Regbaoui, R.: Strong uniqueness for second order differential operators. J. Diff. Eq. 141, 201–217 (1997)CrossRefzbMATHGoogle Scholar
  15. 15.
    Weck, N.: Auß enraumaufgaben in der Theorie stationärer Schwingungen inhomogener elastischer Körper. Math. Z. 111, 387–398 (1969)zbMATHGoogle Scholar
  16. 16.
    Weck, N.: Unique continuation for systems with Lamé principal part. Math. Methods Appl. Sci. 24, 595–605 (2001)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsNational Chung Cheng UniversityChia-YiTaiwan
  2. 2.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan

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