A Remark on the J. L. Lions Lemma and Its Applications in a Variable Exponent Sobolev Space

A Remark on the J. L. Lions Lemma and Its Applications in a Variable Exponent Sobolev Space

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.

Author Details

Junichi Aramaki