Regularization of nonlinear ill-posed problems in Banach spaces and conditional stability

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The main purpose of this research project consists in finding essential progress of knowledge in the field of regularization of nonlinear ill-posed problems in Banach spaces and their crossrelations to the concept of conditional stability. Compared with regularization in Hilbert spaces, considering the regularization of ill-posed operator equations in Banach spaces gives much more freedom that can be used for enforcing a priori information about desired solution properties.A fundamental goal of the project is to get new insight into the impact of smoothness on the quality of regularized solutions for operator equations in Banach spaces. Varying fitting functionals and error measures and their consequences with respect to properties and precision of approximate solutions are components for obtaining progress in this field. We aim to explore the distinguished role of variational inequalities and approximate source conditions intensively studied by the German partners and their strong link to conditional stability for inverse PDE problems well-studied by the Chinese partners as well as consequences for obtaining convergence rates of regularized solutions. This ensures good chances for a significant synergy of such a joint project.