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

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 n...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2023-07, Vol.44 (10), p.987-1011
Main Authors: Nguyen, Hai Son, Dao, Tuan Anh
Format: Article
Language:English
Subjects:
Boundary control
Continuity (mathematics)
Elliptic functions
locally upper Hölder continuity
mixed control-state constraints
optimality condition
solution stability
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Summary: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.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2023.2221739