On Henig Regularization of State-Constrained Optimal Control Problem for the p-Laplace Equation

Abstract

We study a Dirichlet optimal control problem for a quasilinear monotone p-Laplace equation with control and state constraints. The coefficient of the p-Laplacian, the weight u, we take as a control in L1(Ω). We discuss a relaxation of such problem following the so-called Henig regularization scheme.

Keywords

• p-Laplace problem
• optimal control
• control in coecients
• relaxation
• Henig dilating cone
• existence result