On Bitsadze-Samarskii type nonlocal boundary value problems for elliptic differential and difference equations: Well-posedness

Keywords: Elliptic equations Nonlocal boundary value problems Difference schemes Stability a b s t r a c t The well-posedness of the Bitsadze–Samarskii type nonlocal boundary value problem in Hölder spaces with a weight is established. The coercivity inequalities for the solution of the nonlocal boundary value problem for elliptic equations are obtained. The stable second order of accuracy difference scheme for the approximate solution of the problem is presented. The well-posedness of this difference scheme in difference analogue of Hölder spaces is established. For applications, the almost coercivity and the coercivity estimates for solutions of difference schemes for elliptic equations are obtained. The role played by coercive inequalities in the study of local boundary-value problems for elliptic and parabolic differential equations is well known (see, e.g., [1,2]). In the present paper, we consider the Bitsadze–Samarskii type nonlocal boundary value problem