Lagrange multipliers and nonlinear variational inequalities with gradient constraints

The paper deals with nonlinear monotone variational inequalities with gradient constraints. In particular, using a new strong duality principle, the equivalence between the problem under consideration and a suitable double obstacle problem is proved. Moreover, the existence of [Formula: see text] Lagrange multipliers is achieved. This article is part of the theme issue 'Non-smooth variational problems and applications'.