Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

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Cârstea, Cătălin I.; Honda, Naofumi; Nakamura, Gen;
  • Subject: 35J57, 65M32, 75B05 | Mathematics - Analysis of PDEs

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\alpha$, with each $D_\alpha$ a homogeneous elastic medium. One typical example is a finite element mo... View more
  • References (11)
    11 references, page 1 of 2

    [2] G. Alessandrini, K. Kim, Single-logarithmic stability for the Calder´on problem with local data, J. Inverse Ill-Posed Probl. 20 (2012), no. 4, pp. 389-400.

    [3] G. Alessandrini, S. Vessella, Lipschitz stability for the inverse conductivity problem, Adv. in Appl. Math. 35 (2005), no. 2, pp. 207-241.

    [4] E. Beretta, M. de Hoop, L. Qiu, Lipschitz stability of an inverse boundary value problem for a Schr¨odinger-type equation, SIAM J. Math. Anal. 45 (2013), no. 2, pp. 679-699.

    [5] E. Beretta, E. Francini, Lipschitz stability for the electrical impedance tomography problem: the complex case, Comm. Partial Differential Equations 36 (2011), no. 10, 1 pp. 723-1749.

    [6] E. Beretta, E. Francini, A. Morassi, E. Rosset, S. Vessella, Lipschitz continuous dependence of piecewise constant Lam´e coefficients from boundary data: the case of non-flat interfaces, Inverse Problems 30 (2014), no. 12, 125005, 18 pp.

    [7] E. Beretta, E. Francini, S. Vessella, Uniqueness and Lipschitz stability for the identification of Lam´e parameters from boundary measurements, Inverse Probl. Imaging 8 (2014), no. 3, pp. 611-644.

    [8] M. Ikehata, Reconstruction of inclusion from boundary measurements, J. Inv. Ill-Posed Problems, 10 (2002) pp. 37-66.

    [9] G. Nakamura and K. Tanuma,A formula for the fundamental solution of anisotropic elasticity, Q. J. Mech. Appl. Math., 50 (1997) pp. 179-194.

    [10] G. Nakamura and K. Tanuma,Local determination of conductivity at the boundary from the Dirichlet to Neumann map, Inverse Problems, 17 (2001) pp. 405-419.

    [11] G. Nakamura, K. Tanuma and G. Uhlmann, Layer stripping for a transversally isotropic elastic medium, SIAM J. Appl. Math., 59 (1999) pp. 1879-1891.

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