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2013 On an Optimal L 1 -Control Problem in Coefficients for Linear Elliptic Variational Inequality
Olha P. Kupenko, Rosanna Manzo
Abstr. Appl. Anal. 2013: 1-13 (2013). DOI: 10.1155/2013/821964

Abstract

We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients A ( x ) in the main part of the elliptic operator as controls in L 1 ( Ω ; N ( N + 1 ) / 2 ) . Since the eigenvalues of such matrices may vanish and be unbounded in Ω , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called H -admissible solutions.

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Olha P. Kupenko. Rosanna Manzo. "On an Optimal L 1 -Control Problem in Coefficients for Linear Elliptic Variational Inequality." Abstr. Appl. Anal. 2013 1 - 13, 2013. https://doi.org/10.1155/2013/821964

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 07095392
MathSciNet: MR3081614
Digital Object Identifier: 10.1155/2013/821964

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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