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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.

MSC:
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
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[1] DOI: 10.1088/0266-5611/19/4/312 · Zbl 1050.35134 · doi:10.1088/0266-5611/19/4/312
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