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

S. A. Nazarov ; M. V. Olyushin

Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 619-646.

Résumé

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.

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