Volume 56, Issue 3
A Remark on the J. L. Lions Lemma and Its Applications in a Variable Exponent Sobolev Space

Junichi Aramaki

J. Math. Study, 56 (2023), pp. 291-308.

Published online: 2023-07

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  • 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.

  • AMS Subject Headings

35A01, 35D30, 35J62, 35Q61, 35A15

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COPYRIGHT: © Global Science Press

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@Article{JMS-56-291, author = {Aramaki , Junichi}, title = {A Remark on the J. L. Lions Lemma and Its Applications in a Variable Exponent Sobolev Space}, journal = {Journal of Mathematical Study}, year = {2023}, volume = {56}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v56n3.23.03}, url = {http://global-sci.org/intro/article_detail/jms/21874.html} }
TY - JOUR T1 - A Remark on the J. L. Lions Lemma and Its Applications in a Variable Exponent Sobolev Space AU - Aramaki , Junichi JO - Journal of Mathematical Study VL - 3 SP - 291 EP - 308 PY - 2023 DA - 2023/07 SN - 56 DO - http://doi.org/10.4208/jms.v56n3.23.03 UR - https://global-sci.org/intro/article_detail/jms/21874.html KW - J. L. Lions Lemma, de Rham Theorem, Korn inequality, variable exponent Sobolev spaces. AB -

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.

Aramaki , Junichi. (2023). A Remark on the J. L. Lions Lemma and Its Applications in a Variable Exponent Sobolev Space. Journal of Mathematical Study. 56 (3). 291-308. doi:10.4208/jms.v56n3.23.03
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