A Generalized Version of the Lions-Type Lemma

Chmara, Magdalena

doi:10.2478/amsil-2023-0014

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.

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A Generalized Version of the Lions-Type Lemma

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