About homeomorphisms that induce composition operators on Sobolev spaces Academic Article uri icon


  • 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.

publication date

  • January 1, 2010