Lipschitz stability for the electrical impedance tomography problem: The complex case

Communications in Partial Differential Equations

Volumn 36, Issue 10, 2011, Pages 1723-1749

  Beretta, Elena ^a   Francini, Elisa ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Inverse admittivity problem; Lipschitz continuous dependence

Indexed keywords

EID: 80052586085     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605302.2011.552930     Document Type: Article

References (23)

1. Alessandrini, G. (1988). Stable determination of conductivity by boundary measurements. Appl. Anal. 27:153-172.
2. Alessandrini, G., Beretta, E., Rosset, E., Vessella, S. (2001). Optimal stability for inverse elliptic boundary value problems with unknown boundary. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. XXIX:755-806.
3. Alessandrini, G., DiBenedetto, E. (1997). Determining 2-dimensional cracks in 3-dimensional bodies: Uniqueness and stability. Indiana Univ. Math. J. 46:1-82.
4. Alessandrini, G., Vessella, S. (2005). Lipschitz stability for the inverse conductivity problem. Adv. Appl. Math. 35:207-241.
5. Astala, K., Paivarinta, L. (2006). Calderón's inverse conductivity problem in the plane. Ann. Math. 163:265-299.
6. Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2003). Homogenization for electrical conduction in biological tissues in the radio frequency range. Comptes Rendues Mecanique 331:503-508.
7. Amar, M., Andreucci, D., Bisegna, P., Gianni, R. (2009). Exponential asymptotic stability for an elliptic equation with memory arising in electrical conduction in biological tissues. European J. Appl. Math. 20:431-459.
8. Barceló, T., Faraco, D., Ruiz, A. (2007). Stability of Calderón inverse conductivity problem in the plane. J. Math. Pures Appl. 88:522-556.
9. Borcea, L. (2002). Electrical impedance tomography. Inverse Problems 18:R99-R136.
10. Bukhgeim, A.L. (2008). Recovering a potential from Cauchy data in the twodimensional case. J. Inverse Ill-Posed Probl. 16:19-33.
11. Campanato, S. (1980). Sistemi ellittici in forma divergenza. Regolarità all'interno [Elliptic systems in divergence form. Interior regularity]. Pisa: Quaderni della Scuola Normale Superiore di Pisa.
12. Cheney, M., Isaacson, D., Newell, J.C. (1999). Electrical impedance tomography. Siam Review 41:85-101.
13. Dolzmann, G., M̈uller, S. (1995). Estimates for the Green's matrices of elliptic systems by Lp theory. Manuscripta Math. 88:261-273.
14. Dong, H., Kim, S. (2009). Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains. Trans. Amer. Math. Soc. 361:3303-3323.
15. Evans, L.C. (1998). Partial Differential Equations. Graduate Studies in Mathematics, Vol. 19. Providence, RI: AMS.
16. Francini, E. (2000). Recovering a complex coefficient in a planar domain from the Dirichlet-to-Neumann map. Inverse Probl. 16:107-119.
17. Gilbarg, D., Trudinger, N. (1983). Elliptic Partial Differential Equations of Second Order. 2nd ed. Berlin: Springer-Verlag.
18. Hofmann, S., Kim, S. (2007). The Green function estimates for strongly elliptic systems of second order. Manuscripta Math. 124:139-172.
19. Li, Y.Y., Nirenberg, L. (2003). Estimates for elliptic systems from composite material. Comm. Pure Appl. Math. 56:892-925.
20. Littman, W., Stampacchia, G., Weinberger, H.W. (1963). Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17:43-77.
21. Mandache, N. (2001). Exponential instability in an inverse problem for the Schrödinger equation. Inverse Problems 17:1435-1444.
22. Sylvester, J., Uhlmann, G. (1987). A global uniqueness theorem for an inverse boundary value problem. Ann. Math. 125:153-169.
23. Trytten, G.N. (1963). Pointwise bounds for solutions of the Cauchy problem for elliptic equations. Arch. Rat. Mech. Anal. 13:222-244.