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Stable determination of a boundary coefficient in an elliptic equation. (English) Zbl 1155.35108
The paper is motivated by a practical problem of corrosion detection, where the corroded part is inaccessible to direct measurements. The mathematical problem reduces to a Cauchy problem for a second order elliptic problem. In this paper a logarithmic stability estimate for the function representing the amount of corrosion in dependence of a single indirect boundary measurement is derived. The stability result is based on Carleman estimates as used by A. L. Bukhgeim.

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B35 Stability in context of PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
82D35 Statistical mechanical studies of metals
Full Text: DOI
[1] DOI: 10.1088/0266-5611/19/4/312 · Zbl 1050.35134 · doi:10.1088/0266-5611/19/4/312
[2] Bukhgeim A. L., J. Inv. Ill-Posed Probl. 1 pp 17–
[3] DOI: 10.1088/0266-5611/20/1/003 · Zbl 1055.35135 · doi:10.1088/0266-5611/20/1/003
[4] DOI: 10.1088/0266-5611/15/6/303 · Zbl 0943.35100 · doi:10.1088/0266-5611/15/6/303
[5] Cheng J., Numer. Math. J. Chin. Univ. 14 pp 252–
[6] DOI: 10.1088/0266-5611/16/4/101 · Zbl 0957.65052 · doi:10.1088/0266-5611/16/4/101
[7] DOI: 10.1515/1569394042248247 · Zbl 1081.78006 · doi:10.1515/1569394042248247
[8] Choulli M., J. Inv. Ill-Posed Probl. 10 pp 601–
[9] DOI: 10.1088/0266-5611/15/1/008 · Zbl 0922.35188 · doi:10.1088/0266-5611/15/1/008
[10] DOI: 10.1007/978-3-642-61798-0 · Zbl 0361.35003 · doi:10.1007/978-3-642-61798-0
[11] DOI: 10.1088/0266-5611/13/4/006 · Zbl 0882.35133 · doi:10.1088/0266-5611/13/4/006
[12] DOI: 10.1007/s000000050114 · Zbl 0908.35137 · doi:10.1007/s000000050114
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