“…The classical Fourier method is applicable only for solving boundary value and initial boundary value problems for regions of classical shape, which is noted, for example, in solving contact problems [2] for elastic bodies with curvilinear boundaries. The solutions obtained by the classical Fourier method are given, in particular, in the articles [3,4], the application of the method is considered in many books, for example, in [5]. Other areas of development of mathematical tools for solving problems for areas with curvilinear boundaries are associated, first, with the creation and application of a number of methods other than the Fourier method, for example [2,6,7,8], and, secondly, with a modification of the Fourier method itself.…”