Green function of the clamped-free boundary value problem for (-1)M(d/dx)2M on the interval (-1,1) is obtained. Its Green function is a reproducing kernel for a suitable set of Hilbert space and an inner product. By using the fact, the best constant of Sobolev inequality corresponding to this boundary value problem is obtained as a function of M. The best constant is the maximal value of the diagonal value G(y,y) of Green function G(x,y).
Publié le : 2009-10-15
Classification:
Sobolev inequality,
best constant,
Green function,
reproducing kernel,
LU decomposition,
34B05,
34B27,
46E22
@article{1254491215,
author = {Takemura, Kazuo},
title = {The best constant of Sobolev inequality corresponding to clamped-free boundary value problem for (-1)<sup>
M
</sup>(d/dx)<sup>
2M
</sup>},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {85},
number = {2},
year = {2009},
pages = { 112-117},
language = {en},
url = {http://dml.mathdoc.fr/item/1254491215}
}
Takemura, Kazuo. The best constant of Sobolev inequality corresponding to clamped-free boundary value problem for (-1)
M
(d/dx)
2M
. Proc. Japan Acad. Ser. A Math. Sci., Tome 85 (2009) no. 2, pp. 112-117. http://gdmltest.u-ga.fr/item/1254491215/