An elliptic quasi-variational inequality with gradient constraints and some of its applications

We consider a class of quasi-variational inequalities for certain second-or der elliptic operators, where the set of admissible functions is required t o satisfy an implicit gradient bound which depends on the solutions itself. We give sufficient conditions for the existence of a solution, and we appl y our results to stationary problems arising in superconductivity, in therm oplasticity, and in electrostatics with implicit ionization threshold. Copy right (C) 2000 John Wiley & Sons, Ltd.