Optimal \(L^1\)-control in coefficients for Dirichlet elliptic problems: \(H\)-optimal solutions (Q656123)
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scientific article; zbMATH DE number 6000403
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal \(L^1\)-control in coefficients for Dirichlet elliptic problems: \(H\)-optimal solutions |
scientific article; zbMATH DE number 6000403 |
Statements
Optimal \(L^1\)-control in coefficients for Dirichlet elliptic problems: \(H\)-optimal solutions (English)
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26 January 2012
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The paper deals with optimal control problems in coefficients associated with a linear elliptic equation and homogeneous Dirichlet boundary conditions. In particular the coefficient matrix is decomposed having a scalar function as a multiplier which can be degenerate one. The optimal control problem in the coefficient can be stated in different forms depending on the choice of the class of admissible solutions. Using the direct method of the calculus of variations, the solvability of the optimal control problems in the class of \(H\)-admissible solutions is discussed.
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degenerate elliptic equations
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control in coefficients
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weighted Sobolev spaces
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Lavrentiev phenomenon
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direct method in the calculus of variations
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