Inverse problems for nonlinear quasi-variational hemivariational inequalities with application to obstacle problems of elliptic type

Abstract

In this paper we study an inverse problem governed by a constrained nonlinear elliptic quasi-variational hemivariational inequality. The inequality involves two nondifferentiable functions which directly depend on solutions. We solve the direct problem and obtain the properties of weak closedness and uniform boundedness of solutions, which develops some existing results in literature. Then, using a regularized optimization method, we deal with an inverse problem to seek the identification of parameter functions appearing in the leading operator and constraint set. Finally, we apply the abstract result to a concrete inverse problem of identifying the parameter and obstacle functions in elliptic obstacle problems with the p-Laplace operator and mixed boundary conditions.