On Inequalities of Friedrichs and Babuska-Aziz in Dimension Three

Abstract

1983, Horgan and Payne have published a paper entitled "On inequalities of Korn, Friedrichs and Babuska-Aziz". In that paper the two authors have proven a simple relation between the optimal constants occuring in the three inequalities under consideration. The analysis there is restricted to inequalities for functions of two variables only. In the present paper we will show that the results of Horgan and Payne concerning two of the inequalities have a counterpart in dimension three where, however, the situation is different in some aspects.