Identification Elliptic Problem with Dirichlet and Integral Conditions

Abstract

In the present paper, identification elliptic problem in a Hilbert space with Dirichlet and integral boundary conditions is discussed. Identification problem is reduced to auxiliary nonlocal boundary value problem with nonlocal integral condition. Operator approach is used to prove stability and coercive stability inequalities for solution of source identification elliptic problem in the case of a self-adjoint positive definite operator in a differential equation. As applications, four mixed boundary value problems for strongly elliptic multidimensional partial differential equation are investigated. Theorems on stability of solutions of these boundary value problems are established. © 2021, Springer Nature Switzerland AG.