This article is cited in 10 papers

Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system

S. A. Nazarov^a, M. V. Olyushin<sup>b

a</sup> Saint-Petersburg State University
^b Admiral Makarov State Maritime Academy

Abstract: We study the convergence of solutions of boundary value problems for the Lame system under various boundary conditions in the approximation of a smooth contour by polygonal ones. We explain which cases give rise to a paradox similar to that of Sapondzhyan and Babushka. We carry out a formal asymptotic analysis involving a construction of boundary layers near a rapidly oscillating boundary and asymptotic corrections near corner points.The constructed asymptotic behaviour is shown to be valid.

MSC: 73K10

Received: 29.08.1995

DOI: 10.4213/im129

 English version: Izvestiya: Mathematics, 1997, 61:3, 619–646

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