On boundary behavior of spatial mappings

Abstract

We show that homeomorphisms $f$ in ${\mathbb{R}}^n$, $n⩾3$, of finite distortion in the Orlicz--Sobolev classes $W_{\mathrm{loc}}^{1,\phi }$ with a condition on $\phi$ of the Calderon type and, in particular, in the Sobolev classes $W_{\mathrm{loc}}^{1,p}$ for $p>n-1$ are the so-called lower $Q$-homeomorphisms, $Q(x)=K_I^{\frac{1}{n-1}}(x,f)$, 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.

20 pages. arXiv admin note: substantial text overlap with arXiv:1401.4839, arXiv:1012.5010

References in corpus (1)

• On mappings in the Orlicz-Sobolev classes