Abstract
In recent years error bounds for Tikhonov regularization of linear and non-linear ill-posed problems with oversmoothing penalty received attention. Here, oversmoothing means, that the exact solution does not admit a finite value for the used penalty. This problem was initiated by F. Natterer in “Error bounds for Tikhonov regularization in Hilbert scales”. Applicable Anal., 18(1–2):29–37, 1984. In this note we discuss the application of distance functions to derive order optimal error bounds. We specify these bounds in case that the smoothness is given in terms of source conditions.
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