Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system
С. А. Назаров, Maksim Viktorovich Olyushin · Izvestiya Mathematics · 1997
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.