On a technique of finding exact imbedding theorems shown with the example of the anisotropic S. L. Sobolev spaces $W^{L_1,\dots,L_N}_{P_0,\dots,P_N}$ defined on the domains with power boundary and on effects arising in the domains

The paper is devoted to development of a technique of finding exact imbedding theorems shown with the example of the anisotropic S. L. Sobolev spaces denned on the domains with power boundary and to study effects that are possible under certain conditions. Such effects are as follows: 1) the saturation of properties of the type of imbedding theorems with respect to certain differential parameters starting with certain values; 2) the proper space defining the imbeddings differs from a given one and is determined by minimal values of those differential parameters with which the saturation starts; 3) the extention of functions from a given domain to $E^n$ is possible only with the parameters of the proper space; 4) the traces of functions in a given domain are determined by the proper space. Bibliography: 3 titles.