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On unbounded optimal controls in coefficients for ill-posed elliptic dirichlet boundary value problems BOUNDARY VALUE PROBLEMS

Abstract : We consider an optimal control problem associated to Dirichlet boundary value problem for linear elliptic equations on a bounded domain Ω. We take the matrix-valued coecients A(x) of such system as a control in L 1 (Ω; R N × R N). One of the important features of the admissible controls is the fact that the coecient matrices A(x) are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part A sym = (A + A t)/2 may vanish in Ω.
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Thierry Horsin, Peter Kogut. On unbounded optimal controls in coefficients for ill-posed elliptic dirichlet boundary value problems BOUNDARY VALUE PROBLEMS. Вісник Дніпропетровського університету. Серія: Моделювання, 2014, 22 (8), pp.3. ⟨10.15421/141401⟩. ⟨hal-02946721⟩

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