Locally Lipschitz Stability of a Parametric Semilinear Elliptic Optimal Control Problem with Mixed Constraints.

This paper is concerned with the stability of minimizers to a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise control-state constraints. Under the strictly nonnegative second-order optimality condition assumption, we show that the solution map is locally Lipschitz continuous in L 2 - norm as well as in L ∞ - norm of the control variable. [ABSTRACT FROM AUTHOR]