Boundary Value Problems
Volume 2011 (2011), Article ID 875057, 17 pages
The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value Problem
1Department of Computer Science, National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
2Division of Mathematical Sciences, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka 560-8531, Japan
3Tokyo Metropolitan College of Industrial Technology, 1-10-40 Higashi-ooi, Shinagawa, Tokyo 140-0011, Japan
4Department of Liberal Arts and Basic Sciences, College of Industrial Technology, Nihon University, 2-11-1 Shinei, Narashino 275-8576, Japan
Received 14 August 2010; Accepted 10 February 2011
Academic Editor: Irena Rachůnková
Copyright © 2011 Kohtaro Watanabe 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.
Green's function of the clamped boundary value problem for the differential
operator on the interval is obtained. The best constant
of corresponding Sobolev inequality is given by . In addition, it is shown
that a reverse of the Sobolev best constant is the one which appears in the generalized
Lyapunov inequality by Das and Vatsala (1975).