The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value Problem. (7th March 2011)

• Record Type: Journal Article
• Authors: Watanabe, Kohtaro; Kametaka, Yoshinori; Yamagishi, Hiroyuki; Nagai, Atsushi; Takemura, Kazuo
• Other Names: Rachůnková Irena Academic Editor.
• Is Part Of: Boundary value problems. Volume 2011(2011)
• Publication Date: 2011-03-07
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2011/875057
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : Green's functionG(x, y) of the clamped boundary value problem for the differential operator- 1 M d / d x 2 M on the interval(−s, s) is obtained. The best constant of corresponding Sobolev inequality is given bymax | y | ≤ s G(y, y) . 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).