Geodesic
Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system
Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 619-646

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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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     author = {S. A. Nazarov and M. V. Olyushin},
     title = {Approximation of smooth contours by polygonal ones. {Paradoxes} in problems for the {Lame} system},
     journal = {Izvestiya. Mathematics },
     pages = {619--646},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a5/}
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S. A. Nazarov; M. V. Olyushin. Approximation of smooth contours by polygonal ones. Paradoxes in problems for the Lame system. Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 619-646. http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a5/