Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications

Abstract

. 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.