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STABLE DETERMINATION OF A BOUNDARY COEFFICIENT IN AN ELLIPTIC EQUATION

JIN CHENG

School of Mathematical Sciences, Fudan University, Shanghai 200433, China

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MOURAD CHOULLI

Département de Mathématiques Université de Metz, Ile du Saulcy, 57045 Metz cedex 01, France

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JUNSHAN LIN

School of Mathematical Sciences, Fudan University, Shanghai 200433, China

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https://doi.org/10.1142/S0218202508002620Cited by:13 (Source: Crossref)

Abstract

We prove a logarithmic stability estimate for a Cauchy problem associated with a second order elliptic operator. Our proof is essentially based on a Carleman estimate by A. L. Bukhgeim. This result is applied to establish a stability estimate for the inverse problem of determining a boundary coefficient (or a boundary function) by a single boundary measurement. This kind of inverse problems is motivated by the corrosion detection problem.

Keywords:

AMSC: 35R30, 35J05

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