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

الأصل · EN

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<∞) and the pseudo Green matrix G*=A† 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.