A coupled complex boundary method for an inverse conductivity problem with one measurement

References

• Banks HT, K Kunisch. Estimation techniques for distributed parameter systems. Boston (MA): Birkhäuser; 1989.
   Google Scholar
• Chen J, Han W, Schulz F. An asymptotic regularization method for coefficient identification of a generalized nonhomogeneous Helmholtz equation. Japan J. Indust. Appl. Math. 1996;13:51–61.
   Google Scholar
• Engl HW, Hanke M, Neubauer A. Regularization of inverse problems. Dordrecht: Kluwer Academic Publishers Group; 1996.
   Google Scholar
• Isakov V. Inverse problems for partial differential equations. 2nd ed. New York (NY): Springer; 2006.
   Google Scholar
• Liu Y, Zhang X, Lu MW. A meshless method based on least-squares approach for steady-and unsteady-state heat conduction problems. Numer. Heat Transfer Part B. 2005;47:257–275.
   Web of Science ®Google Scholar
• Kohn RV, Vogelius M. Determining conductivity by boundary measurements Commun. Pure Appl. Math. 1984;37:289–298.
   Web of Science ®Google Scholar
• Kohn RV, Vogelius M. Determining conductivity by boundary measurements. II. Interior results. Commun. Pure Appl. Math. 1985;38:643–667.
   Web of Science ®Google Scholar
• Cheney M, Isaacson D, Newell JC. Electrical impedance tomography. SIAM Rev. 1999;41:85–101.
   Web of Science ®Google Scholar
• Borcea L. Electrical impedance tomography. Inverse Probl. 2002;18:R99–R136.
   Web of Science ®Google Scholar
• Lavrentiev MM, Romanov VG, Vasiliev VG. Multidimenional inverse problems for differential equations. Berlin: Springer-Verlag; 1970.
   Google Scholar
• Lions JL. Some aspects of modeling problems in distributed parameter systems. Ruberti A, editor. Proceedings of IFIP working conference, Rome, 1976. Vol. 1, Lecture notes in control and information sciences.Berlin: Springer-Verlag; 1978.
   Google Scholar
• Sylvester J, Uhlmann G. A global uniqueness theorem for an inverse boundary value problem Ann. Math. 1987;125:153–169.
   Google Scholar
• Sun Z, Uhlmann G. Generic uniqueness for an inverse boundary value problem. Duke Math. J. 1991;62:131–155.
   Web of Science ®Google Scholar
• Nachman AI. Global uniqueness for a two-dimensional inverse boundary value problem. Ann. Math. 1995;142:71–96.
   Google Scholar
• Brown R, Uhlmann G. Uniqueness in the inverse conductivity problem for nonsmooth conductivities in two dimensions. Commun. Partial Differ. Equ. 1997;22:1009–1027.
   Web of Science ®Google Scholar
• Astala K, Päivárinta L. Calderón’s inverse conductivity problem in the plane. Ann. Math. 2006;163:265–299.
   Web of Science ®Google Scholar
• Liu L. Stability estimates for the two-dimensional inverse conductivity problem [PhD thesis]. New York (NY): University of Rochester, 1997.
   Google Scholar
• Alessandrini G. Stable determination of conductivity by boundary measurements. Appl. Anal. 1988;27:153–172.
   Google Scholar
• Barceló JA, Barceló T, Ruiz A. Stability of inverse conductivity problem in the plane for less regular conductivities. J. Differ. Equ. 2001;173:231–270.
   Web of Science ®Google Scholar
• Kang H, Seo JK, Sheen D. The inverse conductivity problem with one measurement: stability and estimation of size. SIAM J. Math. Anal. 1997;28:1389–1405.
   Web of Science ®Google Scholar
• Kugler P. Identification for a temperature dependent heat conductivity from single boundary measurements. SIAM J. Numer. Anal. 2003;41:1543–1563.
   Web of Science ®Google Scholar
• Friedman A, Isakov V. On the uniqueness in the inverse conductivity problem with one measurement. Indiana Univ. Math. J. 1989;38:553–579.
   Web of Science ®Google Scholar
• Isakov V, Powell J. On the inverse conductivity problem with one measurement. Inverse Probl. 1990;6:311–318.
   Web of Science ®Google Scholar
• Barceló B, Fabes E, Seo JK. The inverse conductivity problem with one measurement: uniqueness for convex polyhedra. Proc. Am. Math. Soc. 1994;122:183–189.
   Web of Science ®Google Scholar
• Alessandrini G, Isakov V, Powell J. Local uniqueness in the inverse problem with one measurement. Trans. Am. Math. Soc. 1995;347:3031–3041.
   Web of Science ®Google Scholar
• Alessandrini G, Isakov V. Analyticity and uniqueness for the inverse conductivity problem. Rend. Istit. Mat. Univ. Trieste. 1996;28:351–369.
   Google Scholar
• Kang H, Seo JK. Layer potential technique for the inverse conductivity problem. Inverse Probl. 1996;12:227–235.
   Web of Science ®Google Scholar
• Cheng XL, Gong RF, Han W, et al. A novel coupled complex boundary method for inverse source problems. Inverse Probl. 2014;30:055002.
   Web of Science ®Google Scholar
• Dautray R, Lions JL. Mathematical analysis and numerical methods for science and technology. Vol. 2. Berlin: Springer; 1988.
   Google Scholar
• Jin B, Zou J. Numerical estimation of the Robin coefficient in a stationary diffusion equation. IMA J. Numer. Anal. 2010;30:677–701.
   Web of Science ®Google Scholar
• Chen Z, Zou J. An augmented lagrangian method for identifying discontinuous parameters in elliptic systems. SIAM J. Control Optim. 1999;37:892–910.
   Web of Science ®Google Scholar
• Schock E. Arbitrarily slow convergence, uniform convergence and superconvergence of Galerkin-like methods. IMA J. Numer. Anal. 1985;5:153–160.
   Web of Science ®Google Scholar
• Kunisch K, Ring W. Regularization of nonlinear illposed problems with closed operators. Numer. Funct. Anal. Optim. 1993;14:389–404.
   Web of Science ®Google Scholar
• Engl HW, Zou J. A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction. Inverse Probl. 2000;16:1907–1923.
   Web of Science ®Google Scholar
• Lawrence CT, Tits AL. A computationally efficient feasible sequential quadratic programing algorithm. SIAM J. Optim. 2001;11:1092–1118.
   Web of Science ®Google Scholar
• Kang H, Seo JK. Inverse conductivity problem with one measurement: uniqueness of balls in ℝ3 SIAM. J. Appl. Math. 1999;59:1533–1539.
   Web of Science ®Google Scholar
• Kang H, Seo JK, Sheen D. Numerical identification of discontinuous conductivity coefficients Inverse Probl. 1997;13:113–123.
   Google Scholar