Inverse boundary value problems and applications
Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991), Astérisque, no. 207 (1992), pp. 153-211.
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Uhlmann, Gunther. Inverse boundary value problems and applications, in Méthodes semi-classiques Volume 1 - École d'Été (Nantes, juin 1991), Astérisque, no. 207 (1992), pp. 153-211. http://www.numdam.org/item/AST_1992__207__153_0/

[Ag] S. Agmon, Spectral properties of Schrödinger operators and scattering theory, Ann. Scola Norm. Sup. Pisa (4) 2 (1975), 151-218.

[A] L. Ahlfors, Quasiconformal mappings, Van Nostrand, 1966.

[A-N-S] M. Akamatsu, G. Nakamura and S. Steinberg, Identification of Lamé coefficients from boundary observations, to appear Inverse Problems.

[Al] G. Alessandrini, Stable determination of conductivity by boundary measurements, App. Anal., 27 (1988), 153-172.

[A-S] G. Alessandrini and J. Sylvester, Stability for a multidimensional inverse spectral problem, Comm. P.D.E. 15 (1990), 675-692.

[B-C I] R. Beals and R. R. Coifman, Multidimensional inverse scattering and nonlinear PDE, Proc. Symp. Pure Math. 43, American Math. Soc., Providence, (1985), 45-70.

[B-C II] R. Beals and R. R. Coifman, Transformation Spectrales et equation d'evolution non lineares, Seminaire Goulaouic-Meyer-Schwarz, exp 21, 1981-1982.

[C] A. P. Calderón, On an inverse boundary value problem, Seminar on Numerical Analysis and its Applications to Continuum Physics, Soc. Brasileira de Matemática, Río de Janeiro, (1980), 65-73. | MR | Zbl

[Ch] S. Chanillo, A problem in electrical prospection and an $n$-dimensional Borg-Levinson theorem, Proc. AMS, 108, (1990), 761-767. | MR | Zbl

[C-L] R. Courant and P. Lax, The propagation of discontinuities in wave motion, Proc. Nt. Acad. Sci. 42 (1956), 872-876. | DOI | MR | Zbl

[Cu-M I] E. Curtis and J. Morrow, Determining the resistors in a network, SIAM Journal Appl. Math., 50, (1990), 918-930. | DOI | MR | Zbl

[Cu-M II] E. Curtis and J. Morrow, The Dirichlet to Neumann map for a resistor network, to appear SIAM Appl. Math. | MR | Zbl

[F] L. D. Faddeev, Growing solutions of the Schrödinger equation, Dokl. Akad. Nauk SSSR, 165, (1965), 514-517 (translation in Sov. Phys. Dokl. 10, 1033). | Zbl

[F-V] A. Friedman and M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: a continuous dependence result, Arch. Rat. Mech. Anal., 105 (1989), 299-326. | DOI | MR | Zbl

[Ha] R. Hamilton, Harmonic maps of manifolds with boundary, Springer-Verlag Lecture Notes 471, (1975). | MR | Zbl

[H] S. Helgason, The Radon transform, Birkhäuser, Progress in Mathematics 5, Boston, Basel, Stuttgart, (1980). | MR | Zbl

[H-N] G. M. Henkin and R. G. Novikov, A multidimensional inverse problem in quantum and acoustic scattering, Inverse problems, 4, (1988), 103-121. | DOI | MR | Zbl

[I] M. Ikehata, Inversion formulas for the linearized problem for an inverse boundary value problem in elastic prospection, SIAM J. Appl. Math., 50, (1990), 1635-1644. | DOI | MR | Zbl

[Is I] V. Isakov, Completeness of products of solutions and some inverse problems for PDE, to appear Journal Diff. Equations. | MR | Zbl

[Is II] V. Isakov, On uniqueness of recovery of a discontinuous conductivity coefficient, Comm. Pure Appl. Math., 41 (1988), 865-877. | DOI | MR | Zbl

[Is III] V. Isakov, An inverse hyperbolic problem with many boundary measurements, to appear Comm. P.D.E. | MR | Zbl

[Is IV] V. Isakov, On uniqueness in the inverse transmission scattering problem, Comm. P.D.E., 15, (1991), 1565-1588. | DOI | MR | Zbl

[K-M] R. Kohn and A. Mckenney Numerical implementation of a variational method for electrical impedance tomography, preprint | MR | Zbl

[K-V I] R. Kohn and M. Vogelius, Determining conductivity by boundary measurements, Comm. Pure App. Math. 38 (1985), 643-667. | DOI | MR | Zbl

[K-V II] R. Kohn and M. Vogelius, Determining conductivity by boundary measurements II. Interior results, Comm. Pure Appl. Math. 38, 1985, 644-667. | DOI | MR | Zbl

[K-V III] R. Kohn and M. Vogelius, Relaxation of a variational method for impedance computed tomography, Comm. Pure App. Math. 40, (1987), 745-777. | DOI | MR | Zbl

[K-V IV] R. Kohn and M. Vogelius, Identification of an unknown conductivity by means of measurements at the boundary, in Inverse Problems, edited by D. McLaughin, SIAM-AMS Proc. No. 14, Amer. Math. Soc, Providence (1984), 113-123. | MR | Zbl

[L-N I] R. Lavine and A. Nachman, On the inverse scattering transform for the n-dimensional Schrödinger operator, in Topics in solition theory and exactly solvable nonlinear equations, edited by M. Ablowitz, B. Fuchssteiner and M. Kruskal, Oberwolfach, (1986), World Scientific Co. | MR | Zbl

[L-S] G. Lawler and J. Sylvester, Determining resistances from boundary measurements in finite networks, SIAM J. Disc. Math. (1989), 231-239. | DOI | MR | Zbl

[L-M-S-U] J. Lee, G. Mendoza, J. Sylvester, and G. Uhlmann, in preparation

[L-U] J. Lee and G. Uhlmann, Determining anisotropic real-analytic conductivities by boundary measurements, Comm. Pure Appl. Math, 42, (1989) 1097-1112. | DOI | MR | Zbl

[N] A. Nachman, Reconstructions from boundary measurements, Annals of Math., 128 (1988), 531-587. | DOI | MR | Zbl

[N-A] A. Nachman and M. Ablowitz, A multidimensional inverse scattering method, Studies in App. Math. 71 (1984), 243-250. | DOI | MR | Zbl

[N-U] G. Nakamura and G. Uhlmann, Identification of Lame parameters by boundary observations, to appear American Journal of Math. | MR | Zbl

[N-S-U] A. Nachman, J. Sylvester and G. Uhlmann, An $n$-dimensional Borg-Levinson theorem, Comm. Math. Physics 115 (1988), 595-605. | DOI | MR | Zbl

[No] R. Novikov, Multidimensional inverse spectral problems for the equation $-\Delta \psi +\left(\upsilon \left(x\right)-Eu\left(x\right)\right)\psi =0$, Funktsionalny Analizi Ego Prilozheniya, Vol. 22, No. 4, (1988) pp. 11-12, Translation in Functional Analysis and its Applications Vol. 22 No 4 (1988) 263-272. | MR | Zbl

[N-H] R. Novikov and G. Henkin, $\overline{\partial }$-equation in the multidimensional inverse scattering problem, Uspekhi Mat. Nauk Vol. 42 (1987), 93-152 translation in Russian Mathematical Surveys, Vol. 42, No 4, (1987), 109-180. | MR | Zbl

[R I] A. Ramm, Completeness of the products of solutions to PDE and uniqueness theorems in inverse scattering, Inverse problems 3 (1987), (1987), L77-L82. | DOI | MR | Zbl

[R II] A. Ramm, Recovery of the potential from fixed energy scattering data, Inverse Prob. 4 (1988), 877-886. | DOI | MR | Zbl

[R-S] A. Ramm and J. Sjöstrand, An inverse problem of the wave equation, Math. Z., 206, (1991), 119-130. | DOI | EuDML | MR | Zbl

[Ra-S] Rakesh and W. Symes. Uniqueness for an inverse problem for the wave equation, Comm. PDE, 13 (1988), 87-96. | DOI | MR | Zbl

[Sp] M. Spivak, A comprehensive Introduction to Differential Geometry, Vol. II and IV, Publish or Perish. | Zbl

[S] J. Sylvester, An anisotropic inverse boundary value problem, Comm. Pure Appl. Math., (1990), 201-232. | DOI | MR | Zbl

[Su I] Z. Sun, On an inverse boundary value problem in two dimensions, Comm. P.D.E. 14 (1989), 1101-1113. | DOI | MR | Zbl

[Su II] Z. Sun, The inverse conductivity problem in two dimensions, Journal Diff. Equations, 87 (1990), 227-255. | DOI | MR | Zbl

[Su III] Z. Sun, On the continuous dependence for an inverse initial boundary value problem for the wave equation, Journal Math. Anal. Appl., 150, (1990), 188-204. | DOI | MR | Zbl

[Su-U I] Z. Sun and G. Uhlmann, Generic uniqueness for an inverse boundary value problem, Duke Math. Journal, 62 (1991), 131-155. | DOI | MR | Zbl

[Su-U II] Z. Sun and G. Uhlmann, Generic uniqueness for determined inverse problems, to appear Lecture Notes in Math., Springer-Verlag.

[Su-U III] Z. Sun and G. Uhlmann, Inverse scattering for singular potentials in two dimensions, to appear Transactions AMS. | MR | Zbl

[St I] P. Stefanov, Uniqueness of the multidimensional inverse scattering problem for time dependent potentials, Math. Z., 201, (1989), 541-560. | DOI | EuDML | MR | Zbl

[St II] P. Stefanov, to appear Ann. Inst. Fourier Grenoble.

[S-U I] J. Sylvester and G. Uhlmann, Inverse boundary value problems at the boundary - continuous dependence, Comm. Pure Appl. Math. 41 (1988), 197-221. | DOI | MR

[S-U II] J. Sylvester and G. Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. of Math., 125 (1987), 153-169. | DOI | MR | Zbl

[S-U III] J. Sylvester and G. Uhlmann, A uniqueness theorem for an inverse boundary value problem in electrical prospection, Comm. Pure. App. Math., 39 (1986), 91-112. | DOI | MR | Zbl

[S-U IV] J. Sylvester and G. Uhlmann, Remarks on an inverse boundary value problem, in Pseudo-Differential Operators, Oberwolfach 1986, edited by H.O. Cordes, B. Gramsch and H. Widom, Lecture notes in Math. 1256, 430-441. | DOI | MR | Zbl

[S-U V] J. Sylvester and G. Uhlmann, The Dirichlet to Neumann map and applications in Inverse Problems in PDE, Arcata, July-August 1989, edited by D. Colton, R. Ewing and W. Rundell, SIAM Proceedings (1990), 101-139. | MR | Zbl

[S-U VI] J. Sylvester and G. Uhlmann, Inverse problems in anisotropic media, to appear Contemporary Mathematics. | MR | Zbl

[T] F. Treves, Introduction to pseudodifferential and Fourier integral operators, volume 1, New York, Plenum Press, 1980. | MR | Zbl

[W-F-N] A. Wexler, B. Fry and M. Neumann, Impedance-computed tomography algorithm and system, Applied Optics 24 (1985), 3985-3992. | DOI