Methods of obtaining exact embedding theorems in the case of the anisotropic Sobolev spaceW p 0,...p n l 1,...l n (G) defined on a domain with power boundary, and effects arising in the domain (A brief description)

Abstract

The paper is devoted to developing a technique for finding exact embedding theorems shown by the example of the anisotropic Sobolev spaces defined on domains with power boundary and to studying the effects that are possible under certain conditions. Among such effects are (1) the saturation of properties similar to embedding theorems with respect to certain differential parameters, starting with certain values; (2) the true space defining the embeddings differs from the given one and is determined by the minimal values of those differential parameters with which the saturation starts; (3) extension of functions from a given domain to En is possible only with the parameters of the true space; (4) the traces of functions in the given domain are determined by the true space. Bibliography: 3 titles.