Geodesic
Diffraction of the creeping waves from the point of the curvature jump on the boundary of the region (transition of the convex boundary into the concave boundary)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 288-299

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A problem of the diffraction of the creeping waves over-running from the side of the convex boundary to the point of the curvature jump – the point of transition of the convex boundary into the concave boundary is studied. On passing throught the point of the curvature jump, the tangent to the region boundary is changed continiously, but the velocity of this change has the jump. The Green function on the right from the point of the curvature jump has the form of the superposition of the whispering gallery waves. The Dirichlet boundary conditions, the Neumann boundary conditions and the boundary conditions of the impedance kind are considered. The formulas for the boundary current and for the diffraction coefficients received. 
@article{ZNSL_1998_250_a18,
     author = {V. B. Philippov and N. Ya. Kirpichnikova and S. N. Kirpichnikov},
     title = {Diffraction of the creeping waves from the point of the curvature jump on the boundary of the region (transition of the convex boundary into the concave boundary)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {288--299},
     publisher = {mathdoc},
     volume = {250},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a18/}
}
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V. B. Philippov; N. Ya. Kirpichnikova; S. N. Kirpichnikov. Diffraction of the creeping waves from the point of the curvature jump on the boundary of the region (transition of the convex boundary into the concave boundary). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 288-299. http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a18/