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

## TL;DR

This paper investigates an inverse problem for nonlinear quasi-variational inequalities in Banach spaces, developing a regularization framework and applying it to identify material parameters in $p$-Laplacian obstacle problems.

## Contribution

It introduces a novel regularization approach for inverse problems in nonlinear quasi-variational inequalities and applies it to $p$-Laplacian obstacle problems.

## Key findings

- Existence of solutions for the inverse problem established.
- A regularization framework for parameter identification developed.
- Application to $p$-Laplacian obstacle problems demonstrated.

## 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.