Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications
Year: 2022
Author: Junichi Aramaki
Journal of Mathematical Study, Vol. 55 (2022), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n3.22.05
Journal of Mathematical Study, Vol. 55 (2022), Iss. 3 : pp. 281–305
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: J. L. Lions Lemma de Rham Theorem Maxwell-Stokes type problem variable exponent Sobolev spaces multiply connected domain with holes.