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

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.