Year: 2014
Type: preprint
Abstract: We show that homeomorphisms $f$ in ${\Bbb R}^n$, $n\geqslant3$, of finite distortion in the Orlicz--Sobolev classes $W^{1,φ}_{\rm loc}$ with a condition on $φ$ of the Calderon type and, in particular, in the Sobolev classes $W^{1,p}_{\rm loc}$ for $p>n-1$ are the so-called lower $Q$-homeomorphisms, $Q(x)=K^{\frac{1}{n-1}}_I(x,f)$, where $K_I(x,f)$ is its inner dilatation. The statement is valid also for all finitely bi-Lipschitz mappings that a far--reaching extension of the well-known classes of isometric and quasiisometric mappings. This makes pos\-sib\-le to apply our theory of the boundary behavior of the lower $Q$-homeomorphisms to all given classes.
Source: arXiv (Cornell University)
Authors: Kovtonyuk, Denis, Ryazanov, Vladimir
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2264445989