Estimates of deviations from exact solutions of elliptic variational inequalities

In this paper, we present a method of deriving majorants of the difference between exact solutions of elliptic type variational inequalities and any given functions lying in the admissible functional class of the problem under consideration. We analyse three classical problems associated with stationary variational inequalities: a variational problem with two obstacles, elasto-plastic torsion problem and a problem with friction type boundary conditions. The majorants are obtained by a modification of duality technique earlier used for variational problems with uniformly convex functionals [9–11]. These majorants naturally reflects properties of exact solutions and possess necessary continuity conditions.