A New Compactness Theorem for Variational Inequalities of Parabolic Type

This paper is concerned with the weak solvability for fully nonlinear parabolic variational inequalities with time dependent convex constraints. As a possible approach to such problems, there is for instance the fixed point method of the Schauder type with appropriate compactness theorems. However, there has not been prepared any compact‐ ness theorem up to date that enables us the application of the fixed point method to variational inequalities of prabolic type. We have to start establishing a new compactness theorem for a wide class of prabolic variational inequalities.