Hölder stability estimate of Robin coefficient in corrosion detection with a single boundary measurement. (22nd October 2015) - Hu, Guanghui; Yamamoto, Masahiro
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.