SOLUTIONS DIFFERENTIABILITY OF PARAMETRIC OPTIMAL CONTROL FOR ELLIPTIC EQUATIONS

摘要

A family of parameter dependent elliptic optimal control problems with nonlinear boundary control is considered. The control function is subject to amplitude constraints. It is shown that under standard coercivity conditions the solutions to the problems are Bouligand differentiable (in L~s, s < ∞) functions of the parameter. The differentials are characterized as the solutions of accessory linear-quadratic problems.