Abstract
We propose here a new method for the investigation of embedding operators. It is based on an exact description of classes of homeomorphisms that induce change of variables operators on the Sobolev spaces. This method permits to obtain new exact results about embedding operatorsW 1 (G)↪L q (G) (orC(G)) in domainsG ⊂ ℝ n with irregular boundaries. For these types of domains the behavior of the limiting embedding exponentq * (p) is very complicated and surprising. We construct classes of simply connected domains with nonsmooth functionq * (p) and a class of multiply connected domains with discontinuous functionq * (P).
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