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 also supported by the Beibu Gulf University, Project No. 2018KYQD06, Natural Science Foundation of Guangxi (Grant No. 2018JJA110006), and the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0. (29th January 2019) - Migórski, Stanisław; Khan, Akhtar A; Zeng, Shengda
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.