On the openness and discreteness of the mappings satisfying one inequality with respect to $p$-modulus

Abstract

A paper is devoted to study of topological properties of some class of space mappings. It is showed that, sense preserving mappings $f:D\to \overline{{\mathbb{R}}^n}$ of a domain $D\subset {\mathbb{R}}^n,$ $n⩾2,$ satisfying some modulus inequality with respect to $p$-modulus of families of curves, are open and discrete at some restrictions on a function $Q,$ which determinate inequality mentioned above.

arXiv comment13 pages, in Russian

References in corpus (1)

• Sobolev spaces and mappings with bounded (P,Q)-distortion on Carnot groups