A remark on approximation of open sets with regular bounded ones

TL;DR

The paper demonstrates that any open set in Euclidean space can be approximated by an increasing sequence of bounded open sets with analytic boundaries, which may facilitate the study of boundary value problems on irregular domains.

Contribution

It provides a technical result showing the approximation of open sets by bounded sets with analytic boundaries, potentially aiding boundary value problem analysis.

Findings

Any open set in  can be expressed as a union of an ascending sequence of bounded open sets with analytic boundary.

This approximation technique is likely known but is explicitly stated for potential applications.

The result can be useful for studying boundary value problems on irregular open sets.

Abstract

We show that any open set in $\R^n$ is a union of an ascending sequence of bounded open sets with analytic boundary. This is just a technical result, which is probably known. We believe, however, that it can be useful for studing BVPs on irregular open sets.