Weak Optimal Controls in Coefficients for Linear Elliptic Problems

Details Weak Optimal Controls in Coefficients for Linear Elliptic Problems Weak Optimal Controls in Coefficients for Linear Elliptic Problems

2010-12-15

arxiv.org/abs/1012.3290v1

Mathematics

Optimization and Control

11 pages, 0 figures

Scientific paper

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.

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