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

Abstract

We consider a class of quasi-variational inequalities for certain second-order elliptic operators, where the set of admissible functions is required to satisfy an implicit gradient bound which depends on the solutions itself. We give sufficient conditions for the existence of a solution, and we apply our results to stationary problems arising in superconductivity, in thermoplasticity, and in electrostatics with implicit ionization threshold. Copyright © 2000 John Wiley & Sons, Ltd.