On the asymptotic behavior of variational inequalities set in cylinders

We study the asymptotic behavior of solutions to variationalinequalities with pointwise constraint on the value and gradientof the functions as the domain becomes unbounded. First, as amodel problem, we consider the case when the constraint isonly on the value of the functions. Then we consider the more general case ofconstraint also on the gradient. At the end we consider thecase when there is no force termwhich corresponds to Saint-Venantprinciple for linear problems.