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We consider an optimal control problem associated to Dirichlet boundary value problem for linear elliptic equations on a bounded domain Ω. We take the matrixvalued coe cients A(x) of such system as a control in L(Ω;R × R ). One of the important features of the admissible controls is the fact that the coe cient matrices A(x) are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part A = (A+A)/2 may vanish in Ω.

On unbounded optimal controls in coefficients for ill-posed elliptic Dirichlet boundary value problems