On regularity of weighted Sobolev homeomorphisms

TL;DR

This paper investigates the weak regularity properties of inverse mappings of weighted Sobolev homeomorphisms and explores their implications for the composition duality in weighted Sobolev spaces.

Contribution

It establishes the weak regularity of inverse mappings and derives the composition duality property for operators on weighted Sobolev spaces.

Findings

Inverse mappings of weighted Sobolev homeomorphisms exhibit weak regularity.

Derived composition duality property for weighted Sobolev space operators.

Enhanced understanding of the structure of weighted Sobolev homeomorphisms.

Abstract

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