  When describing elastic deformations of a body sometimes it is worth to take
in account elastic spatial dispersion. If spatial dispersion is weak, as
usually happens, then it can be reduced to dependence of thermodynamic
potential on strain gradients. Such a dependence may be worth in association
with small body size which imply large gradients. Besides, the inclusion of
this dispersion leads to physical phenomena absent without it. An example of
the latter is flexoelectricity. Remarkable fact is that while the derivation of
differential equations of elastic equilibrium can be made by ordinary means in
this case, the derivation of boundary conditions for them is less trivial task.
This is due to the fact that strain gradients should be represented in terms of
second gradients of independently varied elastic displacements. Detailed
consideration of this problem is the subject of this paper.
