Spatial behavior in an elastic problem with non-positive definite tensors

The aim of this work is to obtain an alternative of the Phragmén-Lindelöf type for homogeneous elastic materials when the elastic tensor is not positive definite. Indeed, it is necessary to impose some conditions to this tensor in order to prove the estimates. We propose several examples of elastic tensors which are not positive definite but satisfying the above conditions. Finally, the extensions to the three-dimensional and thermoelastic cases are also considered.