Stability Estimates in Determining Robin Coefficients for Biharmonic Inverse Problem

Abstract

We rely on the Carleman estimate and some functional analysis tools to establish a stability result with a logarithmic estimate for an inverse problem governed by the biharmonic equation in a smooth 2D domain \(\Omega \). The inverse problem under consideration consists of recovering Robin’s coefficients on a part \(\Gamma \) of the boundary from a single boundary measurement on the remaining part \(\gamma \) of that boundary. Such inverse problems are usually motivated by the detection of specified functions in beam deflection. The stability result is supported by a numerical example.