On regularity of weighted Sobolev homeomorphisms

We study the weak regularity of mappings inverse to weighted Sobolev homeomorphisms $\phi :\mathrm{\Omega }\to \tilde{\mathrm{\Omega }}$, where $\mathrm{\Omega }$ and $\tilde{\mathrm{\Omega }}$ 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.