An analogue of St. Venant's principle for a polyharmonic equation and applications of it

An a priori energy estimate analogous to the inequalities expressing St. Venant's principle in elasticity theory is obtained for the solution of a polyharmonic equation with the conditions of the first boundary-value problem in an $n$-dimensional domain. These estimates are used to study the behavior of the solution and its derivatives near irregular boundary points and at infinity as a consequence of the geometric properties of the boundary in a neighborhood of these points. Moreover, the estimates obtained are used to prove a uniqueness theorem for the solution of the Dirichlet problem in unbounded domains.
Bibliography: 13 titles.