Correctness of the problem of whispering gallery waves in a neighborhood of points of zero curvature of the boundary

Problems of the propagation of whispering gallery waves in a neighborhood of boundary points where the curvature has a zero of multiplicity one to two are considered. The existence and uniqueness of a solution of these problems are established by means of wave operators.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 261–269, 1979.