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

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.