This paper is devoted to the study of the difference gap (for brevity, D-gap) function and global error bounds for a class of elliptic variational inequalities (for brevity, EVIs). Firstly, we establish the regularized gap function introduced by Yamashita and Fukushima for EVIs under some suitable conditions. Then the D-gap function for EVIs is proposed by employing these regularized gap functions. Furthermore, we also develop the global error bounds for EVIs in terms of the regularized gap function of the Fukushima type and the D-gap function. Finally, an application to frictional contact problem is given to illustrate our main results.

本文致力于研究一类椭圆变分不等式（为简洁，EVI）的差分间隙（D-gap）函数和全局误差界。首先，我们在一些合适的条件下建立了由 Yamashita 和 Fukushima 为 EVI 引入的正则化间隙函数。然后通过使用这些正则化的间隙函数来提出 EVI 的 D 间隙函数。此外，我们还根据福岛型的正则化间隙函数和 D 间隙函数开发了 EVI 的全局误差界限。最后，给出了摩擦接触问题的应用来说明我们的主要结果。