On the module of continuity of mappings with an s-averaged characteristic

We continue studying analytical properties of non-homeomorphic mappings with an s-averaged characteristic. O. Martio proposed the theory of Q-homeomorphisms (2001). The concept of Q-homeomorphisms was extended to maps with branching (2004). In this paper, we study analytical properties of non-homeomorphic mappings with an saveraged characteristic and consider the question of continuity of mappings with an saveraged characteristic. By the well-known Sobolev theorem, a function of class W_s¹_,loc(Rⁿ ) for is equivalent to a continuous function. This property does not hold when s < n. The authors presented such example for mappings with an s-averaged characteristic in 2016. In this paper, we generalize the result obtained earlier to a more general class of mappings with an s-averaged characteristic. Relevant examples are built. The purpose of this paper is to indicate the necessary conditions under which mappings from classes and subclasses of mappings with an s-averaged characteristic 1s¹_,loc(Rⁿ . The theorem is an analogue of the Mori lemma.

Keywords

Authors

References