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State-constrained semilinear elliptic optimization problems with unrestricted sparse controls

  • * Corresponding author: Eduardo Casas

    * Corresponding author: Eduardo Casas

Dedicated to Prof. Dr. Fréderic Bonnans on the occasion of his 60th birthday

The first author was partially supported by Spanish Ministerio de Economía, Industria y Competitividad under projects MTM2014-57531-P and MTM2017-83185-P

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  • In this paper, we consider optimal control problems associated with semilinear elliptic equation equations, where the states are subject to pointwise constraints but there are no explicit constraints on the controls. A term is included in the cost functional promoting the sparsity of the optimal control. We prove existence of optimal controls and derive first and second order optimality conditions. In addition, we establish some regularity results for the optimal controls and the associated adjoint states and Lagrange multipliers.

    Mathematics Subject Classification: Primary: 35J61, 49K20; Secondary: 49J20.


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