TY - JOUR
T1 - About homeomorphisms that induce composition operators on Sobolev spaces
AU - Gol'dshtein, V.
AU - Ukhlov, A.
N1 - Funding Information:
The authors are grateful to the referee for his extremely very useful remarks and suggestions. This work was partially supported by Israel Scientific Foundation (Grant No 1033/07).
PY - 2010/8/1
Y1 - 2010/8/1
N2 - 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 ℝn 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.
AB - 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 ℝn 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.
KW - Composition operators
KW - Mappings of finite distortion
KW - Sobolev spaces
UR - http://www.scopus.com/inward/record.url?scp=77954641005&partnerID=8YFLogxK
U2 - 10.1080/17476930903394705
DO - 10.1080/17476930903394705
M3 - Article
AN - SCOPUS:77954641005
SN - 1747-6933
VL - 55
SP - 833
EP - 845
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 8
ER -