We consider an elliptic boundary value problem with nonlocal conjugation conditions. An a priori estimate for its weak solution in an appropriate Sobolev-like space is proved. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data, is obtained.

中文翻译：

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具有非局部共轭条件的椭圆型二维边值问题

我们考虑具有非局部共轭条件的椭圆边值问题。证明了其在适当的类 Sobolev 空间中的弱解的先验估计。提出并分析了近似该问题的有限差分格式。获得与输入数据的平滑度兼容的收敛速度的估计。