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 - <p style="text-align: justify;">In the author&#39;s previous paper, we considered the equivalent conditions with $W^{-m, p(\cdot )} $-version ($m\ge 0$ integer) of the J. L. Lions Lemma,&nbsp; where $p(\cdot)$ is a variable exponent.&nbsp; 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&nbsp; Korn inequality. Furthermore, we consider the relation to other fundamental results.</p>