Optimal Control by Coefficients in Elliptic Systems

Abstract

Almost all this chapter is concerned with problems of control by coefficients in elliptic systems defined on a bounded domain ft Ω ⊂ ℝ². Nevertheless, the technique developed is easily transferred to the case of Ω ⊂ ℝⁿ where n > 2. One has just to raise either the smoothness index or the degree of integrabihty of elements of a Sobolev space which contains the set of admissible controls.

“‘The time has come, ’ the Walrus said, ‘To talk of many things: Of shoes — and ships — and sealing-wax — Of cabbages — and kings — And why the sea is boiling hot — And whether pigs have wings. ’”

Lewis Carrol

“Through the Looking-Glass”