Geodesic
Difraction on a cone: the asymptotics of the solutions near the vertex
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 122-144

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The mixed problem for the wave equation in a cone $K\subset\mathbb R^n$ is considered. We obtain the asymptotic formulas for the solutions and the Green function near the vertex of the $K$. The properties of the coefficients in the asymptotics connected with the finiteness of the propagation speed are clarified. 
@article{ZNSL_1999_259_a5,
     author = {A. Yu. Kokotov and P. Neittaanm\"aki and B. A. Plamenevskii},
     title = {Difraction on a cone: the asymptotics of the solutions near the vertex},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {122--144},
     publisher = {mathdoc},
     volume = {259},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a5/}
}
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A. Yu. Kokotov; P. Neittaanmäki; B. A. Plamenevskii. Difraction on a cone: the asymptotics of the solutions near the vertex. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 30, Tome 259 (1999), pp. 122-144. http://geodesic.mathdoc.fr/item/ZNSL_1999_259_a5/