Gorbatenko M. Mixed variational approach to estimation of solutions and deterministic data of linear elliptic and parabolic equations under uncertainties

For the first time considered the problem of setting parameters minimax estimation of boundary value problems for linear elliptic and parabolic equations in terms of uncertainty for observations as their solutions, and gradients of these solutions. For systems which are described by the mentioned boundary problems, with quadratic constraints on the unknown deterministic data of these tasks and the second moments of noise in the observations obtained representation for minimax estimates of functionals of solutions and their gradients, as well as the right parts of equations, which are included in the formulation of these problems, through some solutions uniquely solvable systems of mixed variational equations.