<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space.</p>
</abstract>

In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space.

A Generalized Version of the Lions-Type Lemma

Faculty of Applied Physics and Mathematics, Gdańsk University of Technology

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A Generalized Version of the Lions-Type Lemma"}

In this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing...

A Generalized Version of the Lions-Type Lemma

Published Online: Aug 28, 2023

Page range: 240 - 247

Received: Feb 02, 2023

Accepted: Aug 01, 2023

DOI: https://doi.org/10.2478/amsil-2023-0014

Keywords
Lions-type result, concentration-compactness, unbounded domains

© 2023 Magdalena Chmara, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Generalized Version of the Lions-Type Lemma

Published Online: Aug 28, 2023

Page range: 240 - 247

Received: Feb 02, 2023

Accepted: Aug 01, 2023

DOI: https://doi.org/10.2478/amsil-2023-0014

KeywordsLions-type result, concentration-compactness, unbounded domains

© 2023 Magdalena Chmara, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Lions-type result, concentration-compactness, unbounded domains