In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.
@article{SLSEDP_2012-2013____A13_0, author = {Gunther Uhlmann}, title = {30 {Years} of {Calder\'on{\textquoteright}s} {Problem}}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:13}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2012-2013}, doi = {10.5802/slsedp.40}, language = {en}, url = {https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.40/} }
TY - JOUR TI - 30 Years of Calderón’s Problem JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:13 PY - 2012-2013 DA - 2012-2013/// PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.40/ UR - https://doi.org/10.5802/slsedp.40 DO - 10.5802/slsedp.40 LA - en ID - SLSEDP_2012-2013____A13_0 ER -
%0 Journal Article %T 30 Years of Calderón’s Problem %J Séminaire Laurent Schwartz — EDP et applications %Z talk:13 %D 2012-2013 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://doi.org/10.5802/slsedp.40 %R 10.5802/slsedp.40 %G en %F SLSEDP_2012-2013____A13_0
Gunther Uhlmann. 30 Years of Calderón’s Problem. Séminaire Laurent Schwartz — EDP et applications (2012-2013), Talk no. 13, 25 p. doi : 10.5802/slsedp.40. https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.40/
[1] Albin, P, Guillarmou, C., Tzou, L. and Uhlmann, G., Inverse boundary problems for systems in two dimensions, to appear Annales Institut Henri Poincaré.
[2] Alessandrini, G., Stable determination of conductivity by boundary measurements, App. Anal., 27 (1988), 153–172. | MR | Zbl
[3] Alessandrini, G., Singular solutions of elliptic equations and the determination of conductivity by boundary measurements, J. Diff. Equations, 84 (1990), 252-272. | MR | Zbl
[4] Alessandrini, G. and Vessella, S., Lipschitz stability for the inverse conductivity problem, Adv. in Appl. Math., 35 (2005), 207–241. | MR | Zbl
[5] Ammari, H. and Uhlmann, G., Reconstruction of the potential from partial Cauchy data for the Schrödinger equation, Indiana Univ. Math. J., 53 (2004), 169-183. | MR | Zbl
[6] Astala, K. and Päivärinta, L., Calderón’s inverse conductivity problem in the plane. Annals of Math., 163 (2006), 265-299. | MR | Zbl
[7] Astala, K., Lassas, M. and Päiväirinta, L., Calderón’s inverse problem for anisotropic conductivity in the plane, Comm. Partial Diff. Eqns., 30 (2005), 207–224. | MR | Zbl
[8] Bal, G., Ren, K., Uhlmann, G, and Zhou, T., Quantitative thermo-acoustics and related problems, Inverse Problems, 27 (2011), 055007. | MR | Zbl
[9] Bal, G. and Uhlmann, G., Inverse diffusion theory of photoacoustics, Inverse Problems, 26 (2010), 085010. | MR | Zbl
[10] Bal, G. and Uhlmann, G., Reconstructions for some coupled-physics inverse problems, Applied Mathematics Letters, 25 (2012), 1030-1033. | MR | Zbl
[11] Bal, G. and Uhlmann, G., Reconstructions of coefficients in scalar second-order elliptic equations from knowledge of their solutions, to appear Comm. Pure Appl. Math.
[12] Barceló, B., Barceló, J.A., and Ruiz, A., Stability of the inverse conductivity problem in the plane for less regular conductivities, J. Differential Equations, 173 (2001), 231-270. | MR | Zbl
[13] Barceló, J.A., Faraco, D. and Ruiz, A., Stability of Calderón’s inverse problem in the plane, Journal des Mathématiques Pures et Appliquées, 88 (2007), 522-556. | MR | Zbl
[14] Belishev, M. I., The Calderón problem for two-dimensional manifolds by the BC-method, SIAM J. Math. Anal., 35 (2003), 172–182. | MR | Zbl
[15] Blaasten, E, Stability and uniqueness for the inverse problem of the Schrödinger equation with potentials in ${W}^{p,\u03f5}$, arXiv:1106.0632.
[16] Brown, R., Recovering the conductivity at the boundary from the Dirichlet to Neumann map: a pointwise result, J. Inverse Ill-Posed Probl., 9 (2001), 567–574. | MR | Zbl
[17] Brown, R. and Torres, R., Uniqueness in the inverse conductivity problem for conductivities with $3/2$ derivatives in ${L}^{p},p>2n,$ J. Fourier Analysis Appl., 9 (2003), 1049-1056. | Zbl
[18] Brown, R. and Uhlmann, G., Uniqueness in the inverse conductivity problem with less regular conductivities in two dimensions, Comm. PDE, 22 (1997), 1009-10027. | MR
[19] Bukhgeim, A., Recovering the potential from Cauchy data in two dimensions, J. Inverse Ill-Posed Probl., 16 (2008), 19-34. | MR | Zbl
[20] Bukhgeim, A. and Uhlmann, G., Recovering a potential from partial Cauchy data, Comm. PDE, 27 (2002), 653-668. | MR | Zbl
[21] Calderón, A. P., On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), pp. 65–73, Soc. Brasil. Mat., Rio de Janeiro, 1980. | MR
[22] Calderón, A. P., Boundary value problems for elliptic equations. Outlines of the joint Soviet-American symposium on partial differential equations, 303-304, Novisibirsk (1963). | MR
[23] Caro, P., Dos Santos Ferreira, D. and Ruiz, A., Stability estimates for the Radon transform with restricted data and applications, arXiv:1211.1887 (2012).
[24] Caro, P., Garcia, A. and Reyes, J.M., Stability of the Calderón problem for less regular conductivities, J. Differential Equations 254 (2013), 469–492. | MR
[25] Caro, P., Ola, P. and Salo, M., Inverse boundary value problem for Maxwell equations with local data, Comm. PDE, 34 (2009), 1425-1464. | MR | Zbl
[26] Caro, P. and Zhou, T., On global uniqueness for an IBVP for the time-harmonic Maxwell equations, to appear Anal $\&$ PDE, arXiv:1210.7602.
[27] Chanillo S., A problem in electrical prospection and a $n$-dimensional Borg-Levinson theorem, Proc. AMS, 108 (1990), 761–767. | MR | Zbl
[28] Chen, J. and Yang, Y., Quantitative photo-acoustic tomography with partial data, Inverse Problems, 28 (2012), 115014. | MR | Zbl
[29] Chung, F., A partial data result for the magnetic Schrödinger operator, preprint, arXiv:1111.6658.
[30] Dos Santos Ferreira, D., Kenig, C.E., Sjöstrand, J. and Uhlmann, G., Determining a magnetic Schrödinger operator from partial Cauchy data, Comm. Math. Phys., 271 (2007), 467–488. | MR | Zbl
[31] Dos Santos Ferreira, D., Kenig, C.E., Salo, M., and Uhlmann, G., Limiting Carleman weights and anisotropic inverse problems, Inventiones Math., 178 (2009), 119-171. | MR | Zbl
[32] Eskin, G., Ralston, J., On the inverse boundary value problem for linear isotropic elasticity, Inverse Problems, 18 (2002), 907–921. | MR | Zbl
[33] Francini, E., Recovering a complex coefficient in a planar domain from the Dirichlet-to-Neumann map, Inverse Problems, 16 (2000), 107–119. | MR | Zbl
[34] Garcia, A. and Zhang, G., Reconstruction from boundary measurements for less regular conductivities, preprint, arXiv:1212.0727.
[35] Greenleaf, A., Lassas, M. and Uhlmann, G., The Calderón problem for conormal potentials, I: Global uniqueness and reconstruction, Comm. Pure Appl. Math, 56 (2003), 328–352. | MR | Zbl
[36] Greenleaf, A., Lassas, M. and Uhlmann, G., Anisotropic conductivities that cannot be detected in EIT, Physiolog. Meas. (special issue on Impedance Tomography), 24 (2003), 413-420.
[37] Greenleaf, A., Lassas, M. and Uhlmann, G., On nonuniqueness for Calderón’s inverse problem, Math. Res. Lett., 10 (2003), 685-693. | MR | Zbl
[38] Greenleaf, A. and Uhlmann, G., Local uniqueness for the Dirichlet-to-Neumann map via the two-plane transform, Duke Math. J., 108 (2001), 599-617. | MR | Zbl
[39] Guillarmou, C. and Sá Barreto, A., Inverse problems for Einstein manifolds, Inverse Problems and Imaging, 3 (2009), 1-15. | MR | Zbl
[40] Guillarmou, C. and Tzou, L., Calderón inverse problem on Riemann surfaces, Proceedings of CMA, 44 (2009), 129-142. Volume for the AMSI/ANU workshop on Spectral Theory and Harmonic Analysis. | Zbl
[41] Guillarmou, C. and Tzou, L., Calderón inverse problem with partial data on Riemann surfaces, Duke Math. J., 158 (2011), 83-120. | MR | Zbl
[42] Guillarmou, C. and Tzou, L, Identification of a connection from Cauchy data space on a Riemann surface with boundary, Geometric and Functional Analysis (GAFA), 21 (2011), 393-418. | MR
[43] Hähner, P., A periodic Faddeev-type solution operator, J. Differential Equations, 128 (1996), 300–308. | MR | Zbl
[44] Haberman, B. and Tataru, D., Uniqueness in Calderón’s problem with Lipschitz conductivities, to appear Duke Math. J.
[45] Heck, H. and Wang, J.-N., Stability estimates for the inverse boundary value problem by partial Cauchy data, Inverse Problems, 22 (2006), 1787–1796. | MR | Zbl
[46] Henkin, G. and Michel, V., Inverse conductivity problem on Riemann surfaces, J. Geom. Anal., 18 (2008), 1033–1052. | MR | Zbl
[47] Ide, T., Isozaki, H., Nakata S., Siltanen, S. and Uhlmann, G., Probing for electrical inclusions with complex spherical waves, Comm. Pure and Applied Math., 60 (2007), 1415-1442. | MR | Zbl
[48] Ikehata, M., The enclosure method and its applications, Chapter 7 in “Analytic extension formulas and their applications" (Fukuoka, 1999/Kyoto, 2000), Int. Soc. Anal. Appl. Comput., Kluwer Acad. Pub., 9 (2001), 87-103. | MR | Zbl
[49] Imanuvilov, O., Uhlmann, G. and Yamamoto, M., The Calderón problem with partial data in two dimensions, Journal AMS, 23 (2010), 655-691. | MR | Zbl
[50] Imanuvilov, O., Uhlmann, G. and Yamamoto, M., On determination of second order operators from partial Cauchy data, Proceedings National Academy of Sciences., 108 (2011), 467-472. | MR | Zbl
[51] Imanuvilov, O., Uhlmann, G. and Yamamoto, M., Partial data for general second order elliptic operators in two dimensions, Publ. Research Insti. Math. Sci., 48 (2012), 971-1055. | MR
[52] Imanuvilov, O., Uhlmann, G. and Yamamoto, M., Inverse boundary problem with Cauchy data on disjoint sets, Inverse Problems, 27 (2011), 085007. | MR | Zbl
[53] Imanuvilov, O., Uhlmann, G. and Yamamoto, M., On reconstruction of Lamé coefficients from partial Cauchy data in three dimensions, Inverse Problems, 28 (2012), 125002. | MR
[54] Imanuvilov, O., Uhlmann, G. and Yamamoto, M., Inverse boundary value problem by partial data for the Neumann-to-Dirichlet map in two dimensions, preprint, arXiv:1210.1255.
[55] Imanuvilov, O. and Yamamoto, M., Inverse boundary value for Schrödinger equation in two dimensions, arXiv:1211.1419v1.
[56] Imanuvilov, O. and Yamamoto, M., Uniqueness for inverse boundary problems by Dirichlet-to-Neumann map on arbitrary subboundaries, preprint, arXiv:1303.2159. | MR
[57] Isaacson, D., Newell, J. C., Goble, J. C. and Cheney M., Thoracic impedance images during ventilation, Annual Conference of the IEEE Engineering in Medicine and Biology Society, 12 (1990), 106–107.
[58] Isakov, V., On uniqueness in the inverse conductivity problem with local data, Inverse Problems and Imaging, 1 (2007), 95-105. | MR | Zbl
[59] Isakov, V., Nakamura, G., Uhlmann, G. and Wang, J.-N., Increasing stability of the inverse boundary problem for the Schröedinger equation, to appear Contemp. Math., arXiv:1302.0940.
[60] Isozaki, H., Inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in Euclidean space, Amer. J. Math., 126 (2004), 1261–1313. | MR | Zbl
[61] Isozaki, H. and Uhlmann, G., Hyperbolic geometric and the local Dirichlet-to-Neumann map, Advances in Math. 188 (2004), 294-314. | MR | Zbl
[62] Jordana, J., Gasulla, J. M. and Paola’s-Areny, R., Electrical resistance tomography to detect leaks from buried pipes, Meas. Sci. Technol., 12 (2001), 1061-1068.
[63] Jossinet, J., The impedivity of freshly excised human breast tissue, Physiol. Meas., 19 (1998), 61-75.
[64] Kenig, C. and Salo, M., The Calderón problem with partial data on manifolds and applications, preprint, arXiv:1211.1054.
[65] Kenig, C. and Salo, M., Recent progress in the Calderón problem with partial data, preprint, arXiv:1302.4218.
[66] Kenig, C., Salo, M. and Uhlmann, G., Inverse problems for the anisotropic Maxwell equations", Duke Math. J., 157 (2011), 369-419. | MR | Zbl
[67] Kenig, C., Sjöstrand, J. and Uhlmann, G., The Calderón problem with partial data, Annals of Math., 165 (2007), 567-591. | MR | Zbl
[68] Knudsen, K., The Calderón problem with partial data for less smooth conductivities, Comm. Partial Differential Equations, 31 (2006), 57–71. | MR | Zbl
[69] Knudsen, K. and Salo, M., Determining nonsmooth first order terms from partial boundary measurements, Inverse Problems and Imaging, 1 (2007), 349-369. | MR | Zbl
[70] Kocyigit, I., Acoustic-electric tomography and CGO solutions with internal data, Inverse Problems, 28 (2012), 125004. | MR
[71] Kohn, R., Shen, H., Vogelius, M. and Weinstein, M., Cloaking via change of variables in Electrical Impedance Tomography, Inverse Problems 24 (2008), 015016 (21pp). | MR | Zbl
[72] Kohn, R. and Vogelius, M., Identification of an unknown conductivity by means of measurements at the boundary, in Inverse Problems, SIAM-AMS Proc., 14 (1984). | MR | Zbl
[73] Kohn, R. and Vogelius, M., Determining conductivity by boundary measurements, Comm. Pure Appl. Math., 37 (1984), 289–298. | MR | Zbl
[74] Kohn, R. and Vogelius, M., Determining conductivity by boundary measurements II. Interior results, Comm. Pure Appl. Math., 38 (1985), 643–667. | MR | Zbl
[75] Krupchyk, K., Lassas, M. and Uhlmann, G., Inverse problems for differential forms on Riemannian manifolds with boundary, Comm. PDE., 36 (2011), 1475-1509. | MR | Zbl
[76] Krupchyk, K., Lassas, M. and Uhlmann, G., Inverse problems with partial data for the magnetic Schrödinger operator in an infinite slab and on a bounded domain Comm. Math. Phys., 312 (2012), 87-126. | MR | Zbl
[77] Krupchyk, K., Lassas, M. and Uhlmann, G., Inverse boundary value problems for the polyharmonic operator, Journal Functional Analysis, 262 (2012), 1781-1801. | MR | Zbl
[78] Krupchyk, K., Lassas, M. and Uhlmann, G, Determining a first order perturbation of the biharmonic operator by partial boundary measurements, to appear Transactions AMS. | MR
[79] Krupchyk, K., Uhlmann, G, Determining a magnetic Schrödinger operator with a bounded magnetic potential from boundary measurements, preprint, arXiv:1206.4727.
[80] Lassas, M. and Uhlmann, G., Determining a Riemannian manifold from boundary measurements, Ann. Sci. École Norm. Sup., 34 (2001), 771–787. | Numdam | MR | Zbl
[81] Lassas, M., Taylor, M. and Uhlmann, G., The Dirichlet-to-Neumann map for complete Riemannian manifolds with boundary, Comm. Geom. Anal., 11 (2003), 207-222. | MR | Zbl
[82] Lee, J. and Uhlmann, G., Determining anisotropic real-analytic conductivities by boundary measurements, Comm. Pure Appl. Math., 42 (1989), 1097–1112. | MR | Zbl
[83] Li, X. and Uhlmann, G., Inverse problems on a slab, Inverse Problems and Imaging, 4 (2010), 449-462. | MR | Zbl
[84] Mandache, N., Exponential instability in an inverse problem for the Schrödinger equation, Inverse Problems, 17 (2001), 1435–1444. | MR | Zbl
[85] Nachman, A., Global uniqueness for a two-dimensional inverse boundary value problem, Ann. of Math., 143 (1996), 71-96. | MR | Zbl
[86] Nachman, A., Reconstructions from boundary measurements, Ann. of Math., 128 (1988), 531–576. | MR | Zbl
[87] Nachman, A. and Street, B., Reconstruction in the Calderón problem with partial data, Comm. PDE, 35 (2010), 375-390. | MR | Zbl
[88] Nagayasu, S., Uhlmann, G. and Wang, J.-N., Depth dependent stability estimate in electrical impedance tomography, Inverse Problems, 25 (2009), 075001. | MR | Zbl
[89] Nagayasu, S., Uhlmann, G. and Wang, J.-N., Reconstruction of penetrable obstacles in acoustics, SIAM J. Math. Anal., 43 (2011), 189-211. | MR | Zbl
[90] Nagayasu, S, Uhlmann, G. and Wang, J.-N., Increasing stability for the acoustic equation, Inverse Problems, 29 (2013), 020012.
[91] Nakamura, G. and Tanuma, K., Local determination of conductivity at the boundary from the Dirichlet-to-Neumann map, Inverse Problems, 17 (2001), 405–419. | MR | Zbl
[92] Nakamura G. and Uhlmann, G., Global uniqueness for an inverse boundary value problem arising in elasticity, Invent. Math., 118 (1994), 457–474. Erratum: Invent. Math., 152 (2003), 205–207. | Zbl
[93] Nakamura, G., Sun, Z. and Uhlmann, G., Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field, Math. Annalen, 303 (1995), 377–388. | MR | Zbl
[94] Novikov R. G., Multidimensional inverse spectral problems for the equation $-\Delta \psi +\left(v\right(x)-Eu(x\left)\right)\psi =0$, Funktsionalny Analizi Ego Prilozheniya, 22 (1988), 11-12, Translation in Functional Analysis and its Applications, 22 (1988) 263–272. | MR | Zbl
[95] Ola, P., Päivärinta, L. and Somersalo, E., An inverse boundary value problem in electrodynamics, Duke Math. J., 70 (1993), 617–653. | MR | Zbl
[96] Ola, P. and Somersalo, E. , Electromagnetic inverse problems and generalized Sommerfeld potentials, SIAM J. Appl. Math., 56 (1996), 1129-1145 | MR | Zbl
[97] Päivärinta, L., Panchenko, A. and Uhlmann, G., Complex geometrical optics for Lipschitz conductivities, Revista Matematica Iberoamericana, 19 (2003), 57-72. | MR | Zbl
[98] Pestov, L. and Uhlmann, G., Two dimensional simple Riemannian manifolds with boundary are boundary distance rigid,Annals of Math., 161 (2005), 1089-1106. | MR | Zbl
[99] Rondi, L., A remark on a paper by G. Alessandrini and S. Vessella: “Lipschitz stability for the inverse conductivity problem" [Adv. in Appl. Math. 35 (2005), 207–241], Adv. in Appl. Math., 36 (2006), 67–69. | MR | Zbl
[100] Salo, M., Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field, Comm. PDE, 31 (2006), 1639-1666. | MR | Zbl
[101] Salo, M., Inverse problems for nonsmooth first order perturbations of the Laplacian, Ann. Acad. Sci. Fenn. Math. Diss., 139 (2004), 67 pp. | MR | Zbl
[102] Salo, M. and Tzou, L., Inverse problems with partial data for a Dirac system: a Carleman estimate approach, Advances in Math., 225 (2010), 487-513. | MR | Zbl
[103] Salo, M. and Wang, J.-N. , Complex spherical waves and inverse problems in unbounded domains, Inverse Problems 22 (2006), 2299–2309. | MR | Zbl
[104] Siltanen, S., Müller, J. L. and Isaacson, D., A direct reconstruction algorithm for electrical impedance tomography, IEEE Transactions on Medical Imaging, 21 (2002), 555-559.
[105] Somersalo, E., Isaacson, D. and Cheney, M., A linearized inverse boundary value problem for Maxwell’s equations, Journal of Comp. and Appl. Math., 42 (1992),123-136. | MR | Zbl
[106] Sun, Z. and Uhlmann, G., Anisotropic inverse problems in two dimensions, Inverse Problems, 19 (2003), 1001-1010. | MR | Zbl
[107] Sun, Z. and Uhlmann, G., Generic uniqueness for an inverse boundary value problem, Duke Math. Journal, 62 (1991), 131–155. | MR | Zbl
[108] Sylvester, J., An anisotropic inverse boundary value problem, Comm. Pure Appl. Math., 43 (1990), 201–232. | MR | Zbl
[109] Sylvester, J. and Uhlmann, G., A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153–169. | MR | Zbl
[110] Sylvester, J. and Uhlmann, G., A uniqueness theorem for an inverse boundary value problem in electrical prospection, Comm. Pure Appl. Math., 39 (1986), 92–112. | MR | Zbl
[111] Sylvester, J. and Uhlmann, G., Inverse boundary value problems at the boundary – continuous dependence, Comm. Pure Appl. Math., 41 (1988), 197–221. | MR | Zbl
[112] Sylvester, J. and Uhlmann, G., Inverse problems in anisotropic media, Contemp. Math., 122 (1991), 105–117. | MR | Zbl
[113] Takuwa, H., Uhlmann, G. and Wang, J.-N., Complex geometrical optics solutions for anisotropic equations and applications, Journal of Inverse and Ill Posed Problems, 16 (2008), 791-804. 29 (1998), 116–133. | MR | Zbl
[114] Tzou, L., Stability estimates for coefficients of magnetic Schrödinger equation from full and partial measurements, Comm. PDE, 33 (2008), 161-184. | MR | Zbl
[115] Uhlmann, G., Calderón’s problem and electrical impedance tomography, Inverse Problems, 25th Anniversary Volume, 25 (2009), 123011 (39pp.) | Zbl
[116] Uhlmann, G., Editor of Inside Out II: Inverse Problems and Applications, MSRI Publications 60, Cambridge University Press (2012).
[117] Uhlmann, G., Developments in inverse problems since Calderón’s foundational paper, Chapter 19 in “Harmonic Analysis and Partial Differential Equations", University of Chicago Press (1999), 295-345, edited by M. Christ, C. Kenig and C. Sadosky. | MR | Zbl
[118] Uhlmann, G. and Wang, J.-N., Complex spherical waves for the elasticity system and probing of inclusions, SIAM J. Math. Anal., 38 (2007), 1967–1980. | MR | Zbl
[119] Uhlmann, G. and Wang, J.-N., Reconstruction of discontinuities in systems, SIAM J. Appl. Math., 28 (2008), 1026-1044. | MR | Zbl
[120] Uhlmann, G., Wang, J.-N and Wu, C. T., Reconstruction of inclusions in an elastic body, Journal de Mathématiques Pures et Appliquées, 91 (2009), 569-582. | MR | Zbl
[121] Zhdanov, M. S. Keller, G. V., The geoelectrical methods in geophysical exploration, Methods in Geochemistry and Geophysics, 31 (1994), Elsevier.
[122] Zhou, T., Reconstructing electromagnetic obstacles by the enclosure method, Inverse Problems and Imaging, 4 (2010), 547-569. | MR | Zbl
[123] Zou, Y. and Guo, Z, A review of electrical impedance techniques for breast cancer detection, Med. Eng. Phys., 25 (2003), 79-90.
Cited by Sources: