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This paper is devoted to the inverse problem of recovering the unknowndistributed flux on an inaccessible part of boundary using measurement data onthe accessible part. We establish and verify a variational source condition forthis inverse problem, leading to a logarithmic-type convergence rate for thecorresponding Tikhonov regularization method under a low Sobolev regularityassumption on the distributed flux. Our proof is based on the conditionalstability and Carleman estimates together with the complex interpolation theoryon a proper Gelfand triple.

Variational source conditions for the reconstruction of distributed fluxes