2023/04/29 by Bernd Hofmann, Hofmann, Bernd, Chantal Klinkhammer +3 · 1 citation
Computer Science · Engineering · Mathematics · #47A52 #47J06 #65J20 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.2305.00232
openalex publication_date 2023/04/29 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28
In this article on variational regularization for ill-posed nonlinear problems, we are once again discussing the consequences of an oversmoothing penalty term. This means in our model 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, but rarely in a Banach space setting. Our present results try to establish a theoretical justification of oversmoothing regularization in Banach scales. This new study includes convergence rates results for a priori and a posteriori choices of the regularization parameter, both for Hölder-type smoothness and low order-type smoothness. An illustrative example is intended to indicate the specificity of occurring non-reflexive Banach spaces.