Optimal control of partial differential equations

Abstract

In this chapter we will introduce the basic concepts of optimal control for linear elliptic partial differential equations. At first we present the classical theory in functional spaces “à la J.L.Lions”, see [Lio71] and [Lio72]; then we will address the methodology based on the use of the Lagrangian functional (see, e.g., [Mau81], [BKR00] and [Jam88]). Finally, we will show two different numerical approaches for control problems, based on the Galerkin finite element method.