ON THE D-GAP FUNCTIONS FOR VARIATIONAL-HEMIVARIATIONAL INEQUALITIES WITH AN APPLICATION TO CONTACT MECHANICS

The aim of this paper is to investigate the difference gap (for brevity, D-gap) functions and global error bounds for an abstract class of elliptic variational-hemivariational inequalities (for brevity, EVHIs). Based on the optimality condition for the concerning minimization problem, the regularized gap function for EVHIs is proposed under some suitable conditions. Accordingly, we establish the D-gap functions for EVHIs in terms of these regularized gap functions. Furthermore, we provide global error bounds for EVHIs by virtue of the regularized gap functions and the D-gap functions. An application to contact mechanic problem is given to illustrate our main results.