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

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概要

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• 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.

著者

• Yamagishi Hiroyuki

  Tokyo Metropolitan College Of Industrial Technology

• Kametaka Yoshinori

  Osaka City University

• Nagai Atsushi

  Nihon University

• Watanabe Kohtaro

  National Defense Academy

• Takemura Kazuo

  Nihon University

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