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arXiv · 1412.1236

The best constant of discrete Sobolev inequality on the C60 fullerene buckyball

Yoshinori Kametaka·Atsushi Nagai·Hiroyuki Yamagishi·Kazuo Takemura·Kohtaro Watanabe
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Abstract

The best constants of two kinds of discrete Sobolev inequalities on the C60 fullerene buckyball are obtained. All the eigenvalues of discrete Laplacian $A$ corresponding to the buckyball are found. They are roots of algebraic equation at most degree $4$ with integer coefficients. Green matrix $G(a)=(A+a I)^{-1}\ (0<a<\infty)$ and the pseudo Green matrix $G_*=A^{\dagger}$ are obtained by using computer software Mathematica. Diagonal values of $G_*$ and $G(a)$ are identical and they are equal to the best constants of discrete Sobolev inequalities.

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Yoshinori Kametaka, Atsushi Nagai, Hiroyuki Yamagishi, Kazuo Takemura, Kohtaro Watanabe. 2014-12-03. The best constant of discrete Sobolev inequality on the C60 fullerene buckyball. https://arxiv.org/abs/1412.1236

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