On regularity of weighted Sobolev homeomorphisms

Abstract

We study the weak regularity of mappings inverse to weighted Sobolev homeomorphisms $\phi :\Omega \to \tilde{\Omega }$, where $\Omega$ and $\tilde{\Omega }$ are domains in ${\mathbb{R}}^n$. Using the weak regularity of inverse mappings we obtain the composition duality property of composition operators on weighted Sobolev spaces.

20 pages