Product of extension domains is still an extension domain

TL;DR

This paper proves that the product of Sobolev-extension domains retains the extension property, establishing a key stability result in the theory of Sobolev spaces.

Contribution

It demonstrates that the product of extension domains in Sobolev spaces is itself an extension domain, a previously unestablished property.

Findings

Product of Sobolev-extension domains remains an extension domain

Provides a new stability property for Sobolev extension domains

Advances understanding of geometric properties of extension domains

Abstract

We prove the product of the Sobolev-extension domains is still a Sobolev-extension domain.