High Quality Content by WIKIPEDIA articles!In mathematics, the Poincare inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincare. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition. Such bounds are of great importance in the modern, direct methods of the calculus of variations. A very closely related result is the Friedrichs' inequality. The optimal constant C in the Poincare inequality is sometimes known as the Poincare constant for the domain ?. Determining the Poincare constant is, in general, a very hard task that depends upon the value of p and the geometry of the domain ?. Certain special cases are tractable, however. For example, if ? is a bounded, convex, Lipschitz domain with diameter d, then the Poincare constant is at most d/2 for p = 1, d/? for p = 2 (Acosta & Duran 2004; Payne

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.