Nonlocal Optimal Control in the Source—Numerical Approximation of the Compliance Functional Constrained by the p-Laplacian Equation

The goal of this manuscript is the study of an optimal control problem. It consists on the minimization of the compliance functional when the state equation is the nonlocal p-laplacian and the control is the source of this equation. For this problem, a minimum principle, an uniqueness result of optimal control, and a numerical scheme able to approximate the only optimal control, have been derived. The obtained results are an extension of those found in the Cea and Malanowski’s paper, and the arguments employed to face the nonlinear and nonlocal case have been achieved by Muñoz. Some numerical examples are given.