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arXiv · 2211.14211

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

Nguyen Hai Son·Tuan Anh Dao
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Abstract

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 H\"{o}lder continuous in $L^\infty-$norm of control variable when the strictly nonnegative second-order optimality conditions are satisfied for the unperturbed problem.

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Nguyen Hai Son, Tuan Anh Dao. 2022-11-25. Locally H\"{o}lder continuity of the solution map to a boundary control problem with finite mixed control-state constraints. https://arxiv.org/abs/2211.14211

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