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When describing elastic deformations of a body sometimes it is worth to takein account elastic spatial dispersion. If spatial dispersion is weak, asusually happens, then it can be reduced to dependence of thermodynamicpotential on strain gradients. Such a dependence may be worth in associationwith small body size which imply large gradients. Besides, the inclusion ofthis dispersion leads to physical phenomena absent without it. An example ofthe latter is flexoelectricity. Remarkable fact is that while the derivation ofdifferential equations of elastic equilibrium can be made by ordinary means inthis 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 ofsecond gradients of independently varied elastic displacements. Detailedconsideration of this problem is the subject of this paper.

Elastic Boundary Conditions in the Theory with Second Gradients in the Thermodynamic Potential