# A necessary condition on domains for optimal Orlicz-Sobolev embeddings

## TL;DR

This paper establishes a necessary domain regularity condition for the optimal embedding of Orlicz-Sobolev spaces into Orlicz spaces, extending the understanding of functional analysis in these spaces.

## Contribution

It introduces a new necessary condition on domain regularity for optimal Orlicz-Sobolev embeddings, advancing the theoretical framework of functional analysis.

## Key findings

- Identifies a necessary regularity condition for domains
- Extends previous embedding results to Orlicz-Sobolev spaces
- Provides foundational insights for future research in functional analysis

## Abstract

We provide a necessary condition on the regularity of domains for the optimal embeddings of first order (and higher order) Orlicz-Sobolev spaces into Orlicz spaces in the sense of \cite{Cia96} (and \cite{Cia06}).