Open Access
Volume 25, 2019
Article Number 84
Number of page(s) 16
Published online 24 December 2019
  1. L. Afraites, M. Dambrine and D. Kateb, Conformal mapping and inverse conductivity problem with one measurement. ESAIM: COCV. 13 (2007) 163–177. [CrossRef] [EDP Sciences] [Google Scholar]
  2. L. Afraites, M. Dambrine and D. Kateb, Shape methods for the transmission problem with a single measurement. Numer. Funct. Anal. Optim. 28 (2007) 519–551. [Google Scholar]
  3. L. Afraites, M. Dambrine and D. Kateb, On second order shape optimization methods for electrical impedance tomography. SIAM J. Control Optim. 47 (2008) 1556–1590. [Google Scholar]
  4. I. Akduman and R. Kress, Electrostatic imaging via conformal mapping. Inverse Probl. 18 (2002) 1659–1672. [Google Scholar]
  5. G. Alessandrini, V. Isakov and J. Powell, Local uniqueness in the inverse problem with one measurement. Trans. Am. Math. Soc. 347 (1995) 3031–3041. [Google Scholar]
  6. M. Badra, F. Caubet and M. Dambrine, Detecting an obstacle immersed in a fluid by shape optimization methods. Math. Models Methods Appl. Sci. 21 (2011) 2069–2101. [Google Scholar]
  7. M. Brühl, Explicit characterization of inclusions in electrical impedance tomography. SIAM J. Math. Anal. 32 (2001) 1327–1341. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Brühl and M. Hanke, Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Probl. 16 (2000) 1029–1042. [Google Scholar]
  9. R. Chapko and R. Kress, A hybrid method for inverse boundary value problems in potential theory, J. Inv. Ill-Posed Probl. 13 (2005) 27–40. [CrossRef] [Google Scholar]
  10. M. Dambrine, C. Dapogny and H. Harbrecht, Shape optimization for quadratic functionals and states with random right-hand sides. SIAM J. Control Optim. 53 (2015) 3081–3103. [Google Scholar]
  11. M. Dambrine, H. Harbrecht, M. Peters and B. Puig, On Bernoulli’s free boundary problem with a random boundary. Int. J. Uncertain. Quantif . 7 (2017) 335–353. [Google Scholar]
  12. M. Delfour and J.-P. Zolesio, Shapes and Geometries. SIAM, Philadelphia (2001). [Google Scholar]
  13. K. Eppler and H. Harbrecht, A regularized Newton method in electrical impedance tomography using shape Hessian information. Control Cybernet. 34 (2005) 203–225. [Google Scholar]
  14. K. Eppler and H. Harbrecht, Shape optimization for 3D electrical impedance tomography. In R. Glowinski and J. Zolesio, editors, Free and Moving Boundaries: Analysis, Simulation and Control. Vol. 252 of Lecture Notes in Pure and Applied Mathematics. Chapman & Hall/CRC, Boca Raton, FL (2007) 165–184. [CrossRef] [Google Scholar]
  15. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques. Wiley, New York (1968). [Google Scholar]
  16. R. Fletcher, Practical Methods for Optimization. Wiley, New York (1980). [Google Scholar]
  17. A. Friedman and V. Isakov, On the uniqueness in the inverse conductivity problem with one measurement. Indiana Univ. Math. J. 38 (1989) 563–579. [CrossRef] [Google Scholar]
  18. R. Ghanem and P. Spanos, Stochastic finite elements. A Spectral Approach. Springer, New York (1991). [Google Scholar]
  19. C. Grossmann and J. Terno, Numerik der Optimierung. B.G. Teubner, Stuttgart (1993). [Google Scholar]
  20. H. Harbrecht and R. Schneider, Wavelet Galerkin schemes for 2D-BEM. Problems and Methods in Mathematical Physics (Chemnitz, 1999). Edited by J. Elschner, et al. In Vol. 121 of Operator Theory: Advances and Applications. Birkhäuser, Basel (2001) 221–260. [Google Scholar]
  21. F. Hettlich and W. Rundell, The determination of a discontinuity in a conductivity from a single boundary measurement, Inverse Probl. 14 (1998) 67–82. [Google Scholar]
  22. A. Henrot and M. Pierre, Shape Variation and Optimization. In Vol. 28 of Tracts in Mathematics. European Mathematical Society (2017). [Google Scholar]
  23. G. Hsiaoand W. Wendland, A finite element method for some equations of first kind. J. Math. Anal. Appl. 58 (1977) 449–481. [Google Scholar]
  24. R. Kohnand M. Vogelius, Determining conductivity by boundary measurements. Comm. Pure Appl. Math 37 (1984) 289–298. [CrossRef] [MathSciNet] [Google Scholar]
  25. R. Kress, Inverse Dirichlet problem and conformal mapping. Math. Comp. Simul. 66 (2004) 255–265. [CrossRef] [Google Scholar]
  26. W. Lionheart, N. Polydorides and A. Borsic, Electrical impedance tomography: methods, history and applications, edited by D.S. Holder. IOP Series in Medical Physics and Biomedical Engineering. Institute of Physics Publishing (2005) 3–64. [Google Scholar]
  27. M. Loève, Probability theory. I+II. Fourth edn. In Vol. 45 of Graduate Texts in Mathematics. Springer, New York (1977). [Google Scholar]
  28. O. Pironneau, Optimal Shape Design for Elliptic Systems. Springer, New York (1984). [CrossRef] [Google Scholar]
  29. J.-R. Roche and J. Sokolowski, Numerical methods for shape identification problems. Control Cybern. 25 (1996) 867–894. [Google Scholar]
  30. J. Sokolowski and J.-P. Zolesio, Introduction to Shape Optimization. Springer, Berlin (1992). [Google Scholar]

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