Asymptotic Analysis of Elliptic Optimal Control Problems in Thick Multistructures with Dirichlet and Neumann Boundary Controls
In this chapter, we study a class of optimal control problems (OCPs) for a linear elliptic equation in a domain Ω ε ⊂ℝ n (thick multistructure), whose boundary ∂Ω ε contains a very highly oscillating part with respect to ε, as ε→0. We consider this problem assuming that there are two types of the controls active via Neumann and Dirichlet boundary conditions posed on the different parts of the oscillating boundary (for a comparison, see Corbo Esposito, D’Apice, and Gaudiello (2002), De Maio, Gaudiello, and Lefter (2004)).
KeywordsWeak Solution Optimal Control Problem Boundary Control Admissible Control Limit Problem
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