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The local stability of the solution map to a parametric boundary controlproblem governed by semilinear elliptic equations with finite mixed pointwiseconstraints is considered in this paper. We prove that the solution map islocally H\"{o}lder continuous in $L^\infty-$norm of control variable when thestrictly nonnegative second-order optimality conditions are satisfied for theunperturbed problem.

Locally H\"{o}lder continuity of the solution map to a boundary control problem with finite mixed control-state constraints