In this paper we propose the weighted energy method as a way to study estimates of solutions of boundary-value problems with non-homogeneous boundary conditions in elasticity. First, we use this method to study spatial decay estimates in two-dimensional elasticity when we consider non-homogeneous boundary conditions on the boundary. Some comments in the case of harmonic vibrations are considered as well. We also extend the arguments to a class of three-dimensional problems in a cylinder. A section...

A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction $ℱ$ depending on the spatial variable is analysed. It is shown that a solution exists for any $ℱ$ and is globally unique if $ℱ$ is sufficiently small. The Lipschitz continuity of this unique solution as a function of $ℱ$ as well as a function of the load vector $f$ is obtained. Furthermore, local uniqueness of solutions for arbitrary $ℱ>0$ is studied. The question of existence of locally Lipschitz-continuous...