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 $L^1(\Omega)$. 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.
Weak optimal controls in coefficients for linear elliptic problems
BUTTAZZO, GIUSEPPE;
2011-01-01
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 $L^1(\Omega)$. 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.File in questo prodotto:
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