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

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.

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

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• TXT
@Article{CMR-37-209, author = {Junichi and Aramaki and and 14722 and and Junichi Aramaki}, 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.

Junichi Aramaki. (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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