# On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic p-Laplacia

## TL;DR

This paper investigates the existence of optimal controls in a coupled system involving anisotropic p-Laplacian and Hammerstein equations, providing a variational approach and sensitivity analysis for regularized problems.

## Contribution

It establishes the existence of optimal controls for a complex coupled PDE system with nonsmooth coefficients and analyzes their sensitivity to regularization parameters.

## Key findings

- Existence of optimal controls proven for the coupled system.
- Sensitivity analysis conducted for regularized problem variants.
- Framework applicable to anisotropic p-Laplacian systems with nonsmooth controls.

## Abstract

In this paper we consider an optimal control problem for the coupled system of a nonlinear monotone Dirichlet problem with anisotropic p-Laplacian and matrix-valued nonsmooth controls in its coefficients and a nonlinear equation of Hammerstein type. Using the direct method in calculus of variations, we prove the existence of an optimal control in considered problem and provide sensitivity analysis for a specific case of considered problem with respect to two-parameter regularization.