Geodesic
An analogue of St.\,Venant's principle for a polyharmonic equation and applications of~it
Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 237-253

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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. 
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     author = {I. N. Tavkhelidze},
     title = {An analogue of {St.\,Venant's} principle for a polyharmonic equation and applications of~it},
     journal = {Sbornik. Mathematics},
     pages = {237--253},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_46_2_a5/}
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I. N. Tavkhelidze. An analogue of St.\,Venant's principle for a polyharmonic equation and applications of~it. Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 237-253. http://geodesic.mathdoc.fr/item/SM_1983_46_2_a5/