Smooth dependence on parameters of solutions of variational inequalities (Q2488261)

The authors present a result for variational inequalities on closed convex sets in Hilbert spaces that ensures the smooth dependence of the solution with respect to a parameter running in a normed space. The approach consists in showing that, under the imposed assumptions, the variational inequality is locally equivalent to a smooth equation and then applying the implicit function theorem. The result is applied to a model involving a thin beam with finitely many unilateral obstacles at different heights and to Nash equilibria of noncooperative games depending on parameters.