VARIATIONAL INEQUALITIES OF ELLIPTIC AND PARABOLIC TYPE

Abstract

This paper constitutes a short survey of existence methods for variational inequalities of parabolic type. After discussing several illustrative examples in detail, we discuss some of the common methods for proving existence of solutions to such problems: the translation method, Rothe’s method, and the penalty method. As these methods rely on existence results for elliptic variational inequalities, we also provide a summary of basic results and techniques for static problems.