  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.
