On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality

Abstract

In this paper, we consider the equivalent conditions with $L^p$-version ($1 < p < ∞$) of the J.L. Lions lemma. As applications, we first derive the existence of a weak solution to the Maxwell-Stokes type problem and then we consider the Korn inequality. Furthermore, we consider the relation to other fundamental results.