Green function of 2-point simple-type self-adjoint boundary value problem for 4-th order
linear ordinary differential equation, which represents bending of a beam with the
boundary condition as clamped, Dirichlet, Neumann and free. The construction of Green
function needs the symmetric orthogonalization method in some cases. Green function is the
reproducing kernel for suitable set of Hilbert space and inner product. As an application,
the best constants of the corresponding Sobolev inequalities are expressed as the maximum
of the diagonal values of Green function.
Publié le : 2009-12-15
Classification:
Green function,
Sobolev inequality,
best constant,
reproducing kernel,
symmetric orthogonalization method,
34B27,
46E35,
41A44
@article{1267209420,
author = {Takemura, Kazuo and Yamagishi, Hiroyuki and Kametaka, Yoshinori and Watanabe, Kohtaro and Nagai, Atsushi},
title = {The best constant of Sobolev inequality corresponding to a
bending problem of a beam on an interval},
journal = {Tsukuba J. Math.},
volume = {33},
number = {2},
year = {2009},
pages = { 253-280},
language = {en},
url = {http://dml.mathdoc.fr/item/1267209420}
}
Takemura, Kazuo; Yamagishi, Hiroyuki; Kametaka, Yoshinori; Watanabe, Kohtaro; Nagai, Atsushi. The best constant of Sobolev inequality corresponding to a
bending problem of a beam on an interval. Tsukuba J. Math., Tome 33 (2009) no. 2, pp. 253-280. http://gdmltest.u-ga.fr/item/1267209420/