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 - <p style="text-align: justify;">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.</p>