Variational source conditions for the reconstruction of distributed fluxes

Abstract

This paper is devoted to the inverse problem of recovering the unknown distributed flux on an inaccessible part of boundary using measurement data on the accessible part. We establish and verify a variational source condition for this inverse problem, leading to a logarithmic-type convergence rate for the corresponding Tikhonov regularization method under a low Sobolev regularity assumption on the distributed flux. Our proof is based on the conditional stability and Carleman estimates together with the complex interpolation theory on a proper Gelfand triple.