Geodesic
Diffraction of short waves by a contour with H\"{o}lder singularity of curvature. Transition zone
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 43-56

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We consider the short-wave diffraction of a cylindrical wave by a contour whose curvature has a Hölder type discontinuity at a point. The incidence is non-tangent at the point of singularity. In the framework of the Kirchhoff method, we find an asymptotic description for the outgoing wavefield inside the transition zone at both small and moderate distances. Analysis of ray formulas allows us to characterize applicability areas of expressions obtained. 
@article{ZNSL_2021_506_a5,
     author = {E. A. Zlobina},
     title = {Diffraction of short waves by a contour with {H\"{o}lder} singularity of curvature. {Transition} zone},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {43--56},
     publisher = {mathdoc},
     volume = {506},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a5/}
}
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E. A. Zlobina. Diffraction of short waves by a contour with H\"{o}lder singularity of curvature. Transition zone. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 43-56. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a5/