Preprint
Inserted: 13 feb 2010
Year: 2010
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.
Keywords: Degenerate elliptic equations, control in coefficients, weighted Sobolev spaces, Lavrentieff phenomenon
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