Year: 2023
Author: Junichi Aramaki
Journal of Mathematical Study, Vol. 56 (2023), Iss. 3 : pp. 291–308
Abstract
In the author's previous paper, we considered the equivalent conditions with $W^{-m, p(\cdot )} $-version ($m\ge 0$ integer) of the J. L. Lions Lemma, where $p(\cdot)$ is a variable exponent. In this paper, we directly derive $W^{-m,p(\cdot)}$-version of the J. L. Lions Lemma. Therefore, we can use all of the equivalent conditions. As an application, we derive the generalized Korn inequality. Furthermore, we consider the relation to other fundamental results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v56n3.23.03
Journal of Mathematical Study, Vol. 56 (2023), Iss. 3 : pp. 291–308
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: J. L. Lions Lemma de Rham Theorem Korn inequality variable exponent Sobolev spaces.