Well-posedness of a general class of elliptic mixed hemivariational-variational inequalities

In this paper, well-posedness of a general class of elliptic mixed hemivariational- variational inequalities is studied. This general class includes several classes of the previously studied elliptic mixed hemivariational-variational inequalities as special cases. Moreover, our approach of the well-posedness analysis is easily accessible, unlike those in the published papers on elliptic mixed hemivariational- variational inequalities so far. First, prior theoretical results are recalled for a class of elliptic mixed hemivariational-variational inequalities featured by the presence of a potential operator. Then the well-posedness results are extended through a Banach fixed-point argument to the same class of inequalities without the potential operator assumption. The well-posedness results are further extended to a more general class of elliptic mixed hemivariational-variational inequalities through another application of the Banach fixed-point argument. The theoretical results are illustrated in the study of a contact problem. For comparison, the contact problem is studied both as an elliptic mixed hemivariational-variational inequality and as an elliptic variational-hemivariational inequality. (C)& nbsp;2022 Elsevier Ltd. All rights reserved.