On well‐posedness of nonclassical problems for elliptic equations

In the present paper, we consider nonclassical problems for multidimensional elliptic equations. A finite difference method for solving these nonlocal boundary value problems is presented. Stability, almost coercive stability and coercive stability for the solutions of first and second orders of approximation are obtained. The theoretical statements for the solutions of these difference schemes are supported by numerical examples for the two‐dimensional elliptic equations. Copyright © 2014 John Wiley & Sons, Ltd.

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