The Best Constant of Discrete Sobolev Inequality on a Weighted Truncated Tetrahedron

Yoshikatsu Sasaki

Department of Mathematics, Hiroshima University, Higashi-Hiroshima, Japan.

DOI: 10.4236/wjet.2015.33C022                

Abstract

The best constant of discrete Sobolev inequality on the truncated tetrahedron with a weight which describes 2 kinds of spring constants or bond distances. Main results coincides with the ones of known results by Kametaka et al. under the assumption of uniformity of the spring constants. Since the buckyball fullerene C60 has 2 kinds of edges, destruction of uniformity makes us proceed the application to the chemistry of fullerenes.

Keywords

The Best Constant, Sobolev Inequality, Discrete Laplacian, Weighted Graph, Truncated Polyhedron

Conflicts of Interest

The authors declare no conflicts of interest.

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