The optimal constant "C" in the Poincaré inequality is sometimes known as the Poincaré constant for the domain Ω. Determining the Poincaré constant is, in general, a very hard task that depends upon the value of "p" and the geometry of the domain Ω. Certain special cases are tractable, however. For example, if Ω is a bounded, convex, Lipschitz domain with diameter "d", then the Poincaré constant is at most "d"/2 for "p" = 1, formula_10 for "p" = 2 (; ), and this is the best possible estimate on the Poincaré constant in terms of the diameter alone. For smooth functions, this can be understood as an application of the isoperimetric inequality to the function's level sets. [https://web.archive.org/web/20120303090859/http://maze5.net/?page_id=790] In one dimension, this is Wirtinger's inequality for functions.