Perturbation for elliptic variational inequalities (Q1180019)

The author considers a variational inequality, depending on a parameter, in a Hilbert space. First he ``extends'' a result of \textit{S. Dafermos} [Math. Oper. Res. 13, No. 3, 421-434 (1988; Zbl 0674.49007)] claiming that, under the standard coercivity and Lipschitz conditions, and Hausdorff continuity of the map, describing the perturbed convex and closed set, the solution is a continuous function of the parameter (the proof is identical to the proof of Dafermos). Then he presents results concerning continuity of the metric projection on a perturbed set, which follow from the known fact that Mosco convergence is equivalent to convergence of the projection. Some applications to elliptic boundary value problems are given.