Elliptic theta function and the best constants of Sobolev-type inequalities

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概要

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• We obtained the best constants of Sobolev-type inequalities corresponding to higher-order partial differential operators $L=(\partial_t-\Delta+a_0)\cdots(\partial_t-\Delta+a_{M-1})$ and $L_0=(-\Delta+a_0)\cdots(-\Delta+a_{M-1})$ with positive distinct characteristic roots $a_0,\dots,a_{M-1}$, under the suitable assumption on $M$ and $n$. The best constants are given by $L^2$-norm of Green's functions of the boundary value problem $Lu=f(x,t)$ and $L_0 u=f(x)$. The Green's functions are expressed by the elliptic theta function.

• The Japan Society for Industrial and Applied Mathematicsの論文

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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