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Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

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Abstract.

In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Av. Los Castros s/n, 39071 Santander, Spain , , , , , , ES

    E. Casas

  2. Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany , , , , , , DE

    F. Tröltzsch

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  1. E. Casas
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  2. F. Tröltzsch
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Accepted 6 May 1997

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Casas, E., Tröltzsch, F. Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations . Appl Math Optim 39, 211–227 (1999). https://doi.org/10.1007/s002459900104

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  • DOI: https://doi.org/10.1007/s002459900104