Uniqueness for the determination of unknown boundary and impedance with the homogeneous Robin condition

We consider the problem of determining the corroded portion of the boundary of an n-dimensional body (n = 2, 3) and the impedance by two measures on the accessible portion of the boundary. On the unknown boundary part it is assumed the Robin homogeneous condition.

[1]  R. Kress,et al.  Nonlinear integral equations and the iterative solution for an inverse boundary value problem , 2005 .

[2]  Dario Fasino,et al.  An inverse Robin problem for Laplace's equation: theoretical results and numerical methods , 1999 .

[3]  L. Evans.  Measure theory and fine properties of functions , 1992 .

[4]  Sergio Vessella,et al.  Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates , 2007, 0710.2192.

[5]  A. Morassi,et al.  Stable determination of cavities in elastic bodies , 2004 .

[6]  Fadil Santosa,et al.  Nondestructive evaluation of corrosion damage using electrostatic measurements , 1995 .

[7]  H. Fédérer.  Geometric Measure Theory , 1969 .

[8]  Fioralba Cakoni,et al.  Integral equations for inverse problems in corrosion detection from partial Cauchy data , 2007 .

[9]  Elena Beretta,et al.  Stable determination of boundaries from Cauchy data , 1999 .

[10]  G. Alessandrini,et al.  Stable determination of corrosion by a single electrostatic boundary measurement , 2003 .

[11]  H. Weinberger,et al.  Maximum principles in differential equations , 1967 .

[12]  W. Rundell.  Recovering an obstacle and its impedance from Cauchy data , 2008 .

[13]  G. Temple.  Partial Differential Equations of Elliptic Type , 1971 .

[14]  Stability estimates for an inverse elliptic problem , 2002 .

[15]  Mohamed Jaoua,et al.  Identification of Robin coefficients by the means of boundary measurements , 1999 .

[16]  Rainer Kress,et al.  Inverse Dirichlet problem and conformal mapping , 2004, Math. Comput. Simul..

[17]  Luca Rondi,et al.  Optimal Stability for the Inverse Problemof Multiple Cavities , 2001 .

[18]  G. Inglese,et al.  Corrosion detection in conducting boundaries , 2004 .

[19]  S. Vessella.  Unique Continuation Properties and Quantitative Estimates of Unique Continuation for Parabolic Equations , 2009 .