 Friedrichs's inequality is a general case of the Poincaré–Wirtinger inequality which deals with the case "k" = 1.Let formula_1 be a bounded subset of Euclidean space formula_2 with diameter formula_3.Suppose that formula_4 lies in the Sobolev space formula_5, i.e., formula_6 and the trace of formula_7 on the boundary formula_8 is zero.