Skip to main content
SpringerLink
Log in

Strong unique continuation for the Lamé system with Lipschitz coefficients

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alessandrini, G., Morassi, A.: Strong unique continuation for the Lamé system of elasticity. Comm. in. PDE. 26, 1787–1810 (2001)

    MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  4. Garofalo, N., Lin, F.H.: Monotonicity properties of variational integrals, A p weights and unique continuation. Indiana Univ. Math. J. 35, 245–268 (1986)

    MATH  Google Scholar 

  5. Garofalo, N., Lin, F.H.: Unique continuation for elliptic operators: a geometric-variational approach. Comm. in. Pure Appl. Math. 40, 347–366 (1987)

    MATH  Google Scholar 

  6. Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems. Birkhäuser Verlag, 1993

  7. Hörmander, L.: The Analysis of Linear Partial Differential Operators. Vol. III, Springer-Verlag, Berlin/New York, 1985

  8. Hörmander, L.: Uniqueness theorems for second order elliptic differential equations. Comm. in. PDE. 8(1), 21–64 (1983)

    Google Scholar 

  9. Iwaniec, T., Verchota, G., Vogel, A.: The failure of rank-one connections. Arch. Ration. Mech. Anal. 163, 125–169 (2002)

    Article  MATH  Google Scholar 

  10. Lin, C.-L.: Strong unique continuation for an elasticity system with residual stress. Indiana Univ. Math. J. In press

  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)

    MATH  Google Scholar 

  12. Nakamura, G., Wang, J.N.: Unique continuation for the two-dimensional anisotropic elasticity system and its application to inverse problems. Submitted

  13. , 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. Regbaoui, R.: Strong uniqueness for second order differential operators. J. Diff. Eq. 141, 201–217 (1997)

    Article  MATH  Google Scholar 

  15. Weck, N.: Auß enraumaufgaben in der Theorie stationärer Schwingungen inhomogener elastischer Körper. Math. Z. 111, 387–398 (1969)

    MATH  Google Scholar 

  16. Weck, N.: Unique continuation for systems with Lamé principal part. Math. Methods Appl. Sci. 24, 595–605 (2001)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Chung Cheng University, Chia-Yi, 62117, Taiwan

    Ching-Lung Lin

  2. Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan

    Jenn-Nan Wang

Authors
  1. Ching-Lung Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jenn-Nan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jenn-Nan Wang.

Additional information

Mathematics Subject Classification (2000): 35B60, 74B05

Partially supported by the National Science Council of Taiwan, NSC 91-2115-M-002-019.

Acknowledgement We would like to thank anonymous referees for carefully reading the manuscript and for helpful suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, CL., Wang, JN. Strong unique continuation for the Lamé system with Lipschitz coefficients. Math. Ann. 331, 611–629 (2005). https://doi.org/10.1007/s00208-004-0597-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-004-0597-z

Keywords

Search

Navigation