Variational and quasi-variational inequalities with gradient type constraints

This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational inequalities. Motivated by models for critical state problems and applications to free boundary problems in Mechanics and in Physics, in this work several known properties are collected and presented and a few novel results and examples are found