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

Abstract

In this paper we consider an optimal control problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with anisotropic p-Laplacian and matrix-valued \(L^\infty (\varOmega ,\mathbb {R}^{N\times N})\)-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.