Minimax Estimation for Solutions of Transmissions Problems for Elliptic Equations under Absence of Information About Conjugating Conditions

摘要

The minimax estimations for functional from solutions of boundary problems, which describe transmissions for linear elliptic equations of the second order, are obtained on the basis of observations of the systems state. It is provided for the property that conjugating conditions are unknown and relative to right-hand parts of equations, boundary conditions and errors of measuring we know only that they belong to certain given sets. We find systems of integral-differential equations of a special type, which solutions are used for expression of the minimax estimates. Their unique solvability is proved.