Complete low-cut filter and the best constant  of Sobolev inequality

Hiroyuki Yamagishi; Yoshinori Kametaka; Atsushi Nagai; Kohtaro Watanabe; Kazuo Takemura

doi:10.14495/jsiaml.5.33

JSIAM Letters

Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617

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Complete low-cut filter and the best constant of Sobolev inequality

Hiroyuki Yamagishi, Yoshinori Kametaka, Atsushi Nagai, Kohtaro Watanabe, Kazuo Takemura

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Keywords: Sobolev inequality, best constant, Green's function, Bessel function

JOURNAL FREE ACCESS

2013 Volume 5 Pages 33-36

DOI https://doi.org/10.14495/jsiaml.5.33

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Abstract

We obtained the best constants of Sobolev inequalities corresponding to complete low-cut filter. In the background, we have an $n$-dimensional boundary value problem and a one-dimensional periodic boundary value problem. The best constants of the corresponding Sobolev inequalities are equal to diagonal values of Green's functions for these boundary value problems.

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