On the Saint-Venant principle in the case of infinite energy

Estimates on the distribution of the elastic energy in a cylindrical domain in the context of linear elasticity are obtained. The estimates remain valid when the total elastic energy is infinite, and they can be used to establish Saint-Venant's principle without an assumption about finiteness of the total energy. Examples of boundary conditions resulting in infinite energy are constructed in the context of both linear elastostatics and special finite elastostatics, where a quadratic strain energy density function is assumed. The examples show that estimates of the type obtained are sometimes necessary. The results obtained are valid with obvious modifications in a space of any dimension n≥2.