Про Необмежені Оптимальні Керування В Коефіцієнтах Для Погано Обумовлених Еліптичних Крайових Задач

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 matrixvalued 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.