Asymptotics of a solution to the Neumann problem in a thin domain with the sharp edge

S. A. Nazarov   ; Ya. Taskinen

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 193-219

Résumé

The asymptotic expansion of the solution of the Neumann problem for the second order equation in a thin domain with the sharp edge is constructed and justified. Because of the presence of a edge with the zero casp the limit equation on the longitudinal section of a domain obtained as a result of the procedure of lowering a dimention proves to be degenerating and its solution has a nonregular behavior near a boundary.

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