Recovering the conductivity from a single measurement of interior data

Inverse Problems

Volumn 25, Issue 3, 2009, Pages

  Nachman, Adrian ^a   Tamasan, Alexandru ^b   Timonov, Alexandre ^c  

^a UNIVERSITY OF TORONTO   (Canada)

^b UNIVERSITY OF CENTRAL FLORIDA   (United States)

^c UNIVERSITY OF SOUTH CAROLINA UPSTATE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL FEASIBILITY; IDENTIFIABILITY; ITERATIVE RECONSTRUCTION PROCEDURE; NUMERICAL EXPERIMENTS; VOLTAGE POTENTIALS;

EID: 70350333274     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/25/3/035014     Document Type: Article

References (19)

1. Alessandrini G 1986 An identification problem for an elliptic equation in two variables Ann. Mat. Pura Appl. 145 265-95
2. Cheney M and Isaacson D 1991 An overview of inversion algorithms for impedance imaging Contemp. Math. 122 29-39
3. Crandall M G, Ishii H and Lions P-L 1992 User's guide to viscosity solutions of second order partial differential equations Bull. Am. Math. Soc. 27 1-67
4. De Giorgi E 1961 Complementi alla teoria della misura (n - 1)-dimensionale in uno spazio n-dimensionale Sem. Mat. Scuola Norm. Sup. Pisa
5. Federer H 1969 Geometric Measure Theory (Berlin: Springer)
6. Fleming W H and Rishel R 1960 An integral formula for total gradient variation Arch. Math. 11 218-22
7. Gilbarg D and Trudinger N S 2001 Elliptic Partial Differential Equations of Second Order (New York: Springer)
8. Giusti E 1984 Minimal Surfaces and Funcitons of Bounded Variations (Boston: Birkhäuser)
9. Greenberg J M and Harper J R 1981 Algebraic Topology (New York: Benjamin-Cummings)
10. Kim S, Kwon O, Seo J K and Yoon J R 2002 On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography SIAM J. Math. Anal. 34 511-26
11. Ladyzhenskaya O A and Uraltseva N N 1970 Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations Pure Appl. Math. 23 677-703
12. Mandache N 2001 Exponential instability in an inverse problem for the Schrödinger equation Inverse Problems 17 1435-44
13. Nachman A, Tamasan A and Timonov A 2007 Conductivity imaging with a single measurement of boundary and interior data Inverse Problems 23 2551-63
14. Royden H L 1967 Real Analysis (New York: Macmillan)
15. Samarskii A A 2001 The Theory of Difference Schemes (New York: Dekker)
16. Scott G C, Joy M L, Armstrong R L and Henkelman R M 1991 Measurement of nonuniform current density by magnetic resonance IEEE Trans. Med. Imaging 10 362-74
17. Sternberg P and Ziemer W P 1994 Generalized motion by curvature with a Dirichlet condition J. Diff. Eqns 114 580-600
18. Sternberg P and Ziemer W P 1993 The Dirichlet problem for functions of least gradient Degenerate Diffusions (Minneapolis, MN, 1991) (IMA Vol. Math. Appl. vol 47) (New York: Springer) pp 197-214
19. Ziemer W P 1969 Weakly Differentiable Functions (New York: Springer)