Hölder stability estimate of Robin coefficient in corrosion detection with a single boundary measurement. (22nd October 2015)

• Record Type: Journal Article
• Authors: Hu, Guanghui; Yamamoto, Masahiro
• Is Part Of: Inverse problems. Volume 31:Number 11(2015:Nov.)
• Publication Date: 2015-10-22
• Subjects: inverse problem -- corrosion detection -- Robin boundary condition -- reflection principle -- Hölder stability -- elliptic Carleman estimate; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/11/115009
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper is concerned with the inverse problem of detecting a boundary corrosion coefficient which describes some corrosion index from a single pair of Cauchy data measured on an accessible boundary of an electrostatic conductor in two dimensions. The corroded portion is supposed to be either a line segment or a part of some circle, while the corrosion coefficient is restricted to be an analytic or a piecewise constant function. We prove two Hölder stability estimates in recovering the unknown boundary coefficient. Our arguments rely on the Schwarz reflection principle with the Robin boundary condition and a novel interior estimate derived from the elliptic Carleman estimate.