Matrix-Valued L1-Optimal Controls in the Coefficients of linear elliptic problems
Kogut PI, Leugering G (2013)
Publication Type: Journal article, Original article
Publication year: 2013
Journal
Publisher: European Mathematical Society
Book Volume: 32
Pages Range: 433-456
Volume: 32
Issue: 4
Journal Issue: 4
DOI: 10.4171/ZAA/1493
Abstract
We consider optimal control problems for linear degenerate elliptic equations with mixed boundary conditions. In particular, we take the matrix-valued coeffcients A(x) of such systems as controls in L1(;RN(N+1) 2 ). One of the important features of the admissible controls is the fact that eigenvalues of the coeffcient matrices may vanish in Equations of this type may exhibit non-uniqueness of weak solutions. Using the concept of convergence in variable spaces and following the direct method in the Calculus of variations, we establish the solvability of this optimal control problem in the class of weak admissible solutions. © European Mathematical Society.
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APA:
Kogut, P.I., & Leugering, G. (2013). Matrix-Valued L1-Optimal Controls in the Coefficients of linear elliptic problems. Zeitschrift für Analysis und ihre Anwendungen, 32(4), 433-456. https://doi.org/10.4171/ZAA/1493
MLA:
Kogut, Peter I., and Günter Leugering. "Matrix-Valued L1-Optimal Controls in the Coefficients of linear elliptic problems." Zeitschrift für Analysis und ihre Anwendungen 32.4 (2013): 433-456.
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