Geodesic
Paradoxes of limit passage in solutions of boundary value problems involving the approximation of smooth domains by polygonal domains
Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 511-533.

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The Sapondzhyan–Babuska paradox consists in the fact that, when thin circular plates are approximated by regular polygons with freely supported edges, the limit solution does not satisfy the conditions of free support on the circle. In this article, new effects of the same nature are found. In particular, plates with convex holes are considered. Here, in contrast to the case of convex plates, the boundary conditions on the polygon are not preserved in the limit. Methods of approximating a smooth contour leading to passage to the limit from conditions of free support to conditions of rigid support are discussed. Bibliography: 20 titles. 
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V. G. Maz'ya; S. A. Nazarov. Paradoxes of limit passage in solutions of boundary value problems involving the approximation of smooth domains by polygonal domains. Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 511-533. http://geodesic.mathdoc.fr/item/IM2_1987_29_3_a1/

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