Geodesic
Asymptotics of a~solution to the Neumann problem in a~thin domain with the sharp edge
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 193-219

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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. 
@article{ZNSL_2006_332_a12,
     author = {S. A. Nazarov and Ya. Taskinen},
     title = {Asymptotics of a~solution to the {Neumann} problem in a~thin domain with the sharp edge},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {193--219},
     publisher = {mathdoc},
     volume = {332},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a12/}
}
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S. A. Nazarov; Ya. Taskinen. Asymptotics of a~solution to the Neumann problem in a~thin domain with the sharp edge. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 193-219. http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a12/