We derive hierarchical a posteriori error estimates for elliptic variational inequalities. The evaluation amounts to the solution of corresponding scalar local subproblems. We derive some upper bounds for the e ectivity rates and the numerical properties are illustrated by typical examples.

We suggest and analyze some implicit iterative methods for solving the extended general nonconvex variational inequalities using the projection technique. We show that the convergence of these iterative methods requires only the gh-pseudomonotonicity, which is a weaker condition than gh-monotonicity. We also discuss several special cases. Our method of proof is very simple as compared with othe...

In this note we consider a class of environmental games recently proposed in the literature and investigate them by using the powerful tools of variational inequalities. We also consider the case where some data of the problem can depend on a parameter and analyze the regularity of the solution with respect to the parameter. In view of applications to time-dependent or random models, we also in...

We show that the equilibrium state of an infinite system of interacting hard spheres can be obtained in the grand canonical formalism by means of a variational principle. We give also a simple application deriving the Salsburg-Zwanzig-Kirkwood expressions for correlation. functions of the equilibrium state of one dimensional systems of hard spheres. §

In this work we give su cient conditions for the nite convergence of descent algorithms for solving variational inequalities involving generalized monotone mappings.

We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamic formalism for generalized Gibbs states will be discussed. A new class of intuitively Gibbs measures is introduced, and a typical example is studied. Finally, we present a new example of a non-Gibbsian measure arising from an industrial ap...

We consider variational inequalities of higher order with p-growth potentials over a domain in the plane by the way including the obstacle problem for a plate with power hardening law. Using duality methods we prove a posteriori error estimates of functional type for the difference of the exact solution and any admissible comparision function.

We consider vector variational inequalities defined by means of the usual componentwise ordering in a finite dimensional Euclidean space. Our principal result shows that, under suitable convexity assumptions, every weak solution of a vector variational inequality is a strong solution of a reduced variational inequality, obtained from the initial one by considering a selection of components.