The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value Problem. (7th March 2011) - Watanabe, Kohtaro; Kametaka, Yoshinori; Yamagishi, Hiroyuki; Nagai, Atsushi; Takemura, Kazuo
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).