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We consider variational regularization of nonlinear inverse problems inBanach spaces using Tikhonov functionals. This article addresses the problem of$\Gamma$-convergence of a family of Tikhonov functionals and assertions of theconvergence of their respective infima. Such questions arise, if modeluncertainties, inaccurate forward operators, finite dimensional approximationsof the forward solutions and / or data, etc. make the evaluation of theoriginal functional impossible and, thus, its minimizer not computable. But forapplications it is of utmost importance that the minimizer of the replacementfunctional approximates the original minimizer. Under certain additionalconditions this is satisfied if the approximated functionals converge to theoriginal functional in the sense of $\Gamma$-convergence. We deduce simplecriteria in different topologies which guarantee $\Gamma$-convergence as wellas convergence of minimizing sequences.

A note on $\Gamma$-convergence of Tikhonov functionals for nonlinear inverse problems