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Volume 37, Issue 2
On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality

Junichi Aramaki

DOI: 10.4208/cmr.2020-0043

Commun. Math. Res., 37 (2021), pp. 209-235.

Published online: 2021-04

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  • Abstract

In this paper, we consider the equivalent conditions with $L^p$-version ($1 < p < ∞$) of the J.L. Lions lemma. As applications, we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality. Furthermore, we consider the relation to other fundamental results.

  • Keywords

J.L. Lions lemma, de Rham theorem, Maxwell-Stokes type problem, multiply-connected domain.

  • AMS Subject Headings

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

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-37-209, author = {Aramaki , Junichi}, title = {On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {2}, pages = {209--235}, abstract = {

In this paper, we consider the equivalent conditions with $L^p$-version ($1 < p < ∞$) of the J.L. Lions lemma. As applications, we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality. Furthermore, we consider the relation to other fundamental results.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0043}, url = {http://global-sci.org/intro/article_detail/cmr/18738.html} }
TY - JOUR T1 - On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality AU - Aramaki , Junichi JO - Communications in Mathematical Research VL - 2 SP - 209 EP - 235 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/cmr.2020-0043 UR - https://global-sci.org/intro/article_detail/cmr/18738.html KW - J.L. Lions lemma, de Rham theorem, Maxwell-Stokes type problem, multiply-connected domain. AB -

In this paper, we consider the equivalent conditions with $L^p$-version ($1 < p < ∞$) of the J.L. Lions lemma. As applications, we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality. Furthermore, we consider the relation to other fundamental results.

Aramaki , Junichi. (2021). On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality. Communications in Mathematical Research . 37 (2). 209-235. doi:10.4208/cmr.2020-0043
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