On connection of finite distortion mappings with length distortion in $$$\mathbb{R}^n$$$

Ye.A. Sevostianov

doi:10.15421/240917

On connection of finite distortion mappings with length distortion in $$$\mathbb{R}^n$$$

Ye.A. Sevostianov (Institute of Applied Mathematics and Mechanics, NAS of Ukraine), https://orcid.org/0000-0001-7892-6186

Abstract

The present paper is devoted to the investigations of mappings with finite distortion in $$$\mathbb{R}^n$$$, $$$n \geqslant 2$$$. In the work it is proved that every open discrete mapping with finite distortion by Iwaniec such that the branch set of $$$f$$$ is of measure zero is a mapping with finite length distortion provided that the corresponding outer dilatation satisfies the inequality $$$K_O (x, f) \leqslant K(x)$$$ a.e., where $$$K(x) \in L_{loc}^{n-1}(D)$$$.

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