ABSTRACT

The Mathematical Theory of Contact Mechanics is currently emerging as a theory in its own right, as can be seen in the recent monographs [62,107] and the extensive list of references therein, and also in [40,63,71,85,94,95,100]. The present manuscript represents a contribution to the theory. It deals with modeling, applications of variational inequalities and set-valued differential equations, approximate problems, fixed-point theroems, finite element discretization, and optimal order estimates. The number and diversity of mathematical publications dealing with various aspects of the theory is on the increase, and in this short chapter we provide additional references that are directly relevant to the topics studied. We mainly mention the papers where the original results can be found. Then we comment on future directions of development for the theory and present some conclusions.