Abstract
The Bitsadze-Samarskii type nonlocal boundary value problem for the differential equation in a Hilbert space H with the self-adjoint positive definite operator A is considered. The well posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for the solution of the Neumann-Bitsadze-Samarskii type nonlocal boundary value problem for elliptic equations are obtained. The first order of accuracy difference scheme for the approximate solution of this problem is presented. The well posedness of this difference scheme in difference analogue of Hölder spaces is established. In applications, the stability, the almost coercivity and the coercivity estimates for solutions of difference schemes for elliptic equations are obtained.
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