In this paper we investigate the gap functions and regularized gap functions for a class of variational–hemivariational inequalities of elliptic type. First, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the variational–hemivariational inequalities. Then, the global error bounds for such inequalities in terms of regularized gap functions are derived by using the properties of the Clarke generalized gradient. Finally, an application to a stationary nonsmooth semipermeability problem is given to illustrate our main results.

中文翻译：

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变分-半变分不等式的缺口函数和误差界

在本文中，我们研究了一类椭圆型变分半边际不等式的间隙函数和正则间隙函数。首先，基于Yamashita和Fukushima引入的正规化缺口函数，我们为变分半变异不等式建立了一些正规化缺口函数。然后，通过使用Clarke广义梯度的性质，导出针对此类不等式的正则化间隙函数的全局误差范围。最后，给出了对平稳非光滑半渗透性问题的应用，以说明我们的主要结果。