On the J.L. Lions Lemma and Its Applications to the Maxwell-Stokes Type Problem and the Korn Inequality (Communications in Mathematical Research, 2021)
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 weconsider the Korn inequality. Furthermore, we consider the relation to otherfundamental results.
Keywords: J.L. Lions lemma; de Rham theorem; Maxwell-Stokes type problem; multiply-connected domain.