Inverse problems for nonlinear quasi-variational inequalities with an application to implicit obstacle problems of p -Laplacian type**Project supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731 CONMECH, National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, and National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611. It is

Abstract

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