Locally Hölder continuity of the solution map to a boundary control problem with finite mixed control-state constraints

2022/11/25 by Son Hai Nguyen, Son, Nguyen Hai, Tuan Anh Dao +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities #Differential Equations and Numerical Methods #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2211.14211

openalex publication_date 2022/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hölder continuous in L^∞-norm of control variable when the strictly nonnegative second-order optimality conditions are satisfied for the unperturbed problem.

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