an:03979887
Zbl 0606.49017
Casas, Eduardo
Control of an elliptic problem with pointwise state constraints
EN
SIAM J. Control Optimization 24, 1309-1318 (1986).
00151591
1986
j
49K20 35J25 49J20 35B37 35D10 46E35 93C20
pointwise state constraints; elliptic equation of second order; existence and uniqueness; Optimality conditions; regularity
The paper deals with a control problem for an elliptic equation of second order \(Ay=v\) on \(\Omega\), \(y=0\) on \(\partial \Omega\). The cost functional is of the form
\[
J(v)=\int_{\Omega}(y(v)-y_ 0)^ 2dx+(r/2)\int_{\Omega}v^ 2(x)dx,\quad v\in K
\]
where K is a convex closed subset of \(L^ 2(\Omega)\), \(y_ 0\in L^ 2(\Omega)\). The following control problem is solved: minimize J(v) for \(v\in K\) and \(| y(v,x)| \leq 1\) for all \(x\in \Omega.\)
The existence and uniqueness of a solution is proved. Optimality conditions are given and regularity of the optimal solution is investigated.
I.Bock