On the Bitsadze-Samarskii Type Nonlocal Boundary Value Problem with the Integral Condition for an Elliptic Equation

Abstract

In the present paper, the Bitsadze-Samarskii type nonlocal boundary value problem with the integral condition for an abstract elliptic differential equation in a Hilbert space is studied. Theorem on well-posedness of this problem in H\"{o}lder spaces with a weight is established. The nonlocal boundary value problem for multidimensional elliptic equations with the Dirichlet condition is studied. The first order of accuracy difference scheme for the approximate solution of the Bitsadze-Samarskii type nonlocal boundary value problem is investigated. Theorem on well-posedness of this difference scheme in difference analogue of H\"{o}lder spaces with a weight is established.