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The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally Hölder continuous in-norm of control variable when the strictly nonnegative second-order optimality conditions are satisfied for the unperturbed problem.

Locally Hölder Continuity of the Solution Map to a Boundary Control Problem with Finite Mixed Control-State Constraints