Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 34138, 13 pages
On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the
Part of the Boundary with Microinhomogeneous Structure
1Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Moscow 119991, Russia
2Department of Mathematics, Luleå University of Technology, Luleå 97187, Sweden
Received 3 April 2007; Revised 28 June 2007; Accepted 23 October 2007
Academic Editor: Michel Chipot
Copyright © 2007 G. A. Chechkin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the
boundary . It is assumed that consists of pieces with
diameter of order . In addition, and as .