(untitled) (Journal of Mathematical Study, 2022)
We consider the equivalent conditions with W^-m, p(· ) -version of the J. L. Lions Lemma, where p(· ) 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.