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Volume 55, Issue 3
Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications

Junichi Aramaki

DOI: 10.4208/jms.v55n3.22.05

J. Math. Study, 55 (2022), pp. 281-305.

Published online: 2022-09

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  • Abstract

We consider the equivalent conditions with $W^{-m, p(\cdot )} $-version of the J. L. Lions Lemma, where $p(\cdot )$ is a variable exponent satisfying some condition. As applications with $m=0$, we first derive the Korn inequality and furthermore, we consider the relation to other fundamental results. One of the purpose of this paper is an application to the existence of a weak solution for the Maxwell-Stokes type problem.

  • Keywords

J. L. Lions Lemma, de Rham Theorem, Maxwell-Stokes type problem, variable exponent Sobolev spaces, multiply connected domain with holes.

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

aramaki@hctv.ne.jp (Junichi Aramaki)

  • BibTex
  • RIS
  • TXT
@Article{JMS-55-281, author = {Aramaki , Junichi}, title = {Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {3}, pages = {281--305}, abstract = {

We consider the equivalent conditions with $W^{-m, p(\cdot )} $-version of the J. L. Lions Lemma, where $p(\cdot )$ is a variable exponent satisfying some condition. As applications with $m=0$, we first derive the Korn inequality and furthermore, we consider the relation to other fundamental results. One of the purpose of this paper is an application to the existence of a weak solution for the Maxwell-Stokes type problem.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n3.22.05}, url = {http://global-sci.org/intro/article_detail/jms/20977.html} }
TY - JOUR T1 - Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications AU - Aramaki , Junichi JO - Journal of Mathematical Study VL - 3 SP - 281 EP - 305 PY - 2022 DA - 2022/09 SN - 55 DO - http://doi.org/10.4208/jms.v55n3.22.05 UR - https://global-sci.org/intro/article_detail/jms/20977.html KW - J. L. Lions Lemma, de Rham Theorem, Maxwell-Stokes type problem, variable exponent Sobolev spaces, multiply connected domain with holes. AB -

We consider the equivalent conditions with $W^{-m, p(\cdot )} $-version of the J. L. Lions Lemma, where $p(\cdot )$ is a variable exponent satisfying some condition. As applications with $m=0$, we first derive the Korn inequality and furthermore, we consider the relation to other fundamental results. One of the purpose of this paper is an application to the existence of a weak solution for the Maxwell-Stokes type problem.

Junichi Aramaki. (2022). Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications. Journal of Mathematical Study. 55 (3). 281-305. doi:10.4208/jms.v55n3.22.05
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