Stability for an inverse boundary problem of determining a part of a boundary

Inverse Problems

Volumn 15, Issue 4, 1999, Pages 1021-1032

  Bukhgeim, A L ^a   Cheng, J ^b,c   Yamamoto, M ^d  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^b FUDAN UNIVERSITY   (China)

^c GUNMA UNIVERSITY   (Japan)

^d UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001191809     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/15/4/312     Document Type: Article

References (21)

1. Alessandrini G 1993 Stable determination of a crack from boundary measurements Proc. R. Soc. Edinb. A 123 497-516
2. Alessandrini G 1997 Examples of instability in inverse boundary-value problems Inverse Problems 13 887-97
3. Alessandrini G and Rondi L 1998 Stable determination of a crack in a planar inhomogeneous conductor SIAM J. Math. Anal. 30 326-40
4. Beretta E and Vessella S 1998 Stable determination of boundaries from Cauchy data SIAM J. Math Anal. 30 220-32
5. Bukhgeim A L 1993 Extension of solutions of elliptic equations from discrete sets J. Inverse Ill-Posed Prob. 1 17-32
6. Bukhgeim A L and Kardakov B V 1998 Stability for the inverse problem of finding the boundary condition J. Inverse Ill-Posed Prob. 309-18
7. Cheng J and Yamamoto M 1998 Unique continuation on a line for harmonic functions Inverse Problems 14 869-82
8. Colton D L 1980 Analytic Theory of Partial Differential Equations (Boston, MA: Pitman)
9. Gilberg D and Trudinger N S 1977 Elliptic Partial Differential Equations of Second Order (Berlin: Springer)
10. Isakov V 1993 New stability results for soft obstacles in inverse scattering Inverse Problems 9 535-43
11. John F 1960 Continuous dependence on data for solutions of partial differential equations with a prescribed bound Commun. Pure Appl. Math. 13 551-85
12. Kaup P G, Santosa F and Vogelius M 1996 Method for imaging corrosion damage in thin plates from electrostatic data Inverse Problems 12 279-93
13. Landis E M 1963 Some problems of the qualitative theory of second order elliptic equations (case of several independent variables) Russ. Math. Surv. 18 1-62
14. Lavrentiev M M 1967 Some Improperly Posed Problems of Mathematical Physics (Berlin: Springer) (Engl. transl.)
15. Lions J L and Magenes E 1972 Non-homogeneous Boundary Value Problems and Applications (Berlin: Springer)
16. Micheal D H, Waechter R T and Collins R 1982 The measurement of surface cracks in metals by using a.c. electric fields Proc. R. Soc. Lond. A 381 139-57
17. Payne L E 1960 Bounds in the Cauchy problem for the Laplace equation Arch. Ration. Mech. Anal. 5 35-45
18. Ramm A G 1994 Stability of the solution to inverse obstacle scattering problem J. Inverse Ill-Posed Prob. 2 269-75
19. Rauch J 1991 Partial Differential Equations (Berlin: Springer)
20. Rondi L 1998 Uniqueness and stability for the determination of boundary defects by electrostatic measurements Preprint SISSA-ISAS 73/98/AF (Trieste, Italy, July)
21. Rondi L Optimal stability estimates for the determination of defects by electrostatic measurements Preprint