About homeomorphisms that induce composition operators on Sobolev spaces

作者：Gol'dshtein V^*; Ukhlov A

来源：Complex Variables and Elliptic Equations, 2010, 55(8-10): 833-845.

DOI：10.1080/17476930903394705

• Sobolev spaces
• composition operators
• mappings of finite distortion

We study generalizations of the quasiconformal homeomorphisms (the so-called homeomorphisms with bounded (p, q)-distortion) that induce bounded composition operators on the Sobolev spaces with the first weak derivatives. If a homeomorphism between domains of the Euclidean space R(n) has bounded (p, q)-distortion and q>n - 1 then its inverse mapping has bounded (q/(q - n + 1), p/(p - n + 1))-distortion. In this article, we study in detail the analytical properties of these homeomorphisms in the limit case q = n - 1. The study of these classes is important because of applications of mappings with bounded (p, q)-distortion to the Sobolev type embedding theorems and nonlinear elasticity problems.

• 出版日期2010