Variational source conditions for inverse Robin and flux problems by partial measurements

This work is devoted to the convergence analysis of the Tikhonov regularization for the inverse Robin and flux problems.Both inverse problems aim at recovering a respective physical quantity on an inaccessible part of the boundary through some measurement on a partial accessible boundary.The convergence and convergence rate in the desirable L²-norm are derived based on two new logarithmic type stabilities (only in some weak norms,e.g.,the negative Sobolev norms), which enable us to construct and rigorously verify the required variational source conditions. Addendum: The abstract is added since it was missing when the article was published online. To reflect this addition an Addendum is published in this same IPI 16-2 April 2022 regular issue. We apologize for any inconvenience this may cause.