Non-compact embeddings of Sobolev spaces

The paper deals with the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set, and gives an example in which the embedding is not strictly singular. The same is shown to hold when the open set is an infinite strip.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The paper discusses the embedding of a first-order Sobolev space in a Lebesgue space on a bounded open set and provides an example where the embedding is not strictly singular. The same result is shown to hold when the open set is an infinite strip.