Calculus of Variations and Geometric Measure Theory

G. Buttazzo - P. Kogut

Weak Optimal Controls in Coefficients for Linear Elliptic Problems

created by buttazzo on 13 Feb 2010



Inserted: 13 feb 2010

Year: 2010


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