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The primary objective of this research is to investigate an inverse problemof parameter identification in nonlinear mixed quasi-variational inequalitiesposed in a Banach space setting. By using a fixed point theorem, we exploreproperties of the solution set of the considered quasi-variational inequality.We develop a general regularization framework to give an existence result forthe inverse problem. Finally, we apply the abstract framework to a concreteinverse problem of identifying the material parameter in an implicit obstacleproblem given by an operator of $p$-Laplacian type.

Inverse Problems for Nonlinear Quasi-Variational Inequalities with an Application to Implicit Obstacle Problems of $p$-Laplacian Type