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Weak optimal controls in coefficients for linear elliptic problems

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Abstract

In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions. We adopt the weight function as a control in L 1(Ω). Using the direct method in the Calculus of variations, we discuss the solvability of this optimal control problem in the class of weak admissible solutions.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    Giuseppe Buttazzo

  2. Department of Differential Equations, Dnipropetrovsk National University, Naukova str. 13, 49050, Dnipropetrovsk, Ukraine

    Peter I. Kogut

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  1. Giuseppe Buttazzo
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  2. Peter I. Kogut
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Correspondence to Giuseppe Buttazzo.

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Buttazzo, G., Kogut, P.I. Weak optimal controls in coefficients for linear elliptic problems. Rev Mat Complut 24, 83–94 (2011). https://doi.org/10.1007/s13163-010-0030-y

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  • DOI: https://doi.org/10.1007/s13163-010-0030-y

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