In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on 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. Our present study tries to continue and to extend those investigations to Banach scales. This new study includes convergence rates results for a priori choices of the regularization parameter, both for H\"older-type smoothness and low order-type smoothness. The necessary tools for low order smoothness in the Banach space setting are provided.

翻译：在目前的工作中,我们讨论对弊病非线性问题的变通正规化问题,重点是过缓的处罚术语。这意味着,在我们的模式中,寻找非线性操作员等式解决办法不属于刑罚定义的功能范围。在过去几年中,在希尔伯特的尺度中全面调查了这种变通化的正规化问题。我们的研究试图继续并将这些调查扩大到班纳奇的尺度。这项新的研究包括预先选择正规化参数的趋同率结果,既包括H\“老式平滑和低顺序型平滑。提供了班纳赫空间设置中低秩序平稳的必要工具。