New results for variational regularization with oversmoothing penalty term in Banach spaces
Bernd Hofmann1, Chantal Klinkhammer2, Robert Plato3
1Chemnitz University of Technology, Germany; 2University of Siegen, Germany; 3University of Siegen, Germany
In this talk on variational regularization for ill-posed nonlinear problems, we discuss the impact of utilizing an oversmoothing penalty term. This means that the searched-for solution of the considered nonlinear operator equation does not belong to the domain of definition of the penalty functional. In the past years, such variational regularization has been investigated comprehensively in Hilbert scales. Our present results extents those results to Banach scales. This new study includes convergence rates results for a priori and a posteriori choices of the regularization parameter, both for H\"older-type smoothness and low order-type smoothness. An illustrative example intends to indicate the specific characteristics of non-reflexive Banach spaces.