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Upper Semicontinuity of the Solution Map to a Parametric Elliptic Optimal Control Problem

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Abstract

This paper studies solution stability of a parametric optimal control problem governed by semilinear elliptic equations and nonconvex objective function with mixed pointwise constrains in which the controls act both in the domain and on the boundary. We give sufficient conditions under which the solution map is upper semicontinuous and continuous in parameters.

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Acknowledgments

The authors wish to express their sincere thanks to the anonymous referees for their helpful suggestions and useful comments which improved the original manuscript greatly. The research is funded by the Hanoi University of Science and Technology (HUST) under grant number T2017-PC-073.

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Authors and Affiliations

  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Vietnam

    N. H. Son

  2. Faculty of Information Technology, National University of Civil Engineering, 55 Giai Phong Str, Hanoi, Vietnam

    N. B. Giang

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  1. N. H. Son
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  2. N. B. Giang
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Correspondence to N. H. Son.

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Son, N.H., Giang, N.B. Upper Semicontinuity of the Solution Map to a Parametric Elliptic Optimal Control Problem. Set-Valued Var. Anal 29, 257–282 (2021). https://doi.org/10.1007/s11228-020-00546-0

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  • DOI: https://doi.org/10.1007/s11228-020-00546-0

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