Lipschitz continuous dependence of piecewise constant Lamé coefficients from boundary data: the case of non-flat interfaces

We consider the inverse problem of determining the Lame moduli for a piecewise constant elasticity tensor , where is a known finite partition of the body Ω, from the Dirichlet-to-Neumann map. We prove that Lipschitz stability estimates can be derived under regularity assumptions on the interfaces.

[1]  Masaru Ikehata,et al.  Inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection , 1990 .

[2]  James Ralston,et al.  On the inverse boundary value problem for linear isotropic elasticity , 2002 .

[3]  Giovanni Alessandrini,et al.  Stable determination of conductivity by boundary measurements , 1988 .

[4]  G. Alessandrini,et al.  STRONG UNIQUE CONTINUATION FOR THE LAMÉ SYSTEM OF ELASTICITY* , 2001 .

[5]  Antonino Morassi,et al.  Stable Determination of an Inclusion in an Elastic Body by Boundary Measurements , 2013, SIAM J. Math. Anal..

[6]  Brian Malcolm Brown,et al.  A variational approach to an elastic inverse problem , 2005 .

[7]  Sergio Vessella,et al.  Lipschitz stability for the inverse conductivity problem , 2005, Adv. Appl. Math..

[8]  Elena Beretta,et al.  Uniqueness and Lipschitz stability for the identification of Lam\'e parameters from boundary measurements , 2013, 1303.2443.

[9]  Louis Nirenberg,et al.  Estimates for elliptic systems from composite material , 2003 .

[10]  A. Kirsch,et al.  Inverse problems for abstract evolution equations with applications in electrodynamics and elasticity , 2016 .

[11]  S. Bagdasarov Proof of the Main Result , 1998 .

[12]  Luca Rondi,et al.  The stability for the Cauchy problem for elliptic equations , 2009, 0907.2882.

[13]  G. Uhlmann,et al.  Inverse problems at the boundary for an elastic medium , 1995 .

[14]  Gunther Uhlmann,et al.  On uniqueness of Lamé coefficients from partial Cauchy data in three dimensions , 2012, 1205.4436.

[15]  G. Uhlmann,et al.  IDENTIFICATION OF LAME PARAMETERS BY BOUNDARY MEASUREMENTS , 1993 .

[16]  Feng,et al.  Methods for identifying sub-regional material parameters of concrete dams using modal data , 2003 .

[17]  G. Uhlmann,et al.  Global uniqueness for an inverse boundary value problem arising in elasticity , 1994 .

[18]  V. Zvyagin,et al.  Attractors of equations of non-Newtonian fluid dynamics , 2014 .

[19]  Niculae Mandache,et al.  Exponential instability in an inverse problem for the Schrodinger equation , 2001 .

[20]  Sergio Vessella,et al.  Lipschitz stability for a stationary 2D inverse problem with unknown polygonal boundary , 2006 .