Kametaka, Yoshinori; Watanabe, Kohtaro; Nagai, Atsushi; Takemura, Kazuo; Yamagishi, Hiroyuki Positivity and hierarchical structure of four Green functions corresponding to a bending problem of a beam on a half line. (English) Zbl 1516.34056 Math. J. Okayama Univ. 65, 145-173 (2023). Reviewer: Tatuana Badokina (Saransk) MSC: 34B27 34B40 PDFBibTeX XMLCite \textit{Y. Kametaka} et al., Math. J. Okayama Univ. 65, 145--173 (2023; Zbl 1516.34056) Full Text: DOI
Takemura, Kazuo; Nagai, Atsushi; Kametaka, Yoshinori; Watanabe, Kohtaro; Yamagishi, Hiroyuki Sobolev inequality of free boundary value problem for \((-1)^{M}(d/dx)^{2M}\). (English) Zbl 1335.46032 J. Inequal. Appl. 2015, Paper No. 54, 20 p. (2015). MSC: 46E35 34B27 PDFBibTeX XMLCite \textit{K. Takemura} et al., J. Inequal. Appl. 2015, Paper No. 54, 20 p. (2015; Zbl 1335.46032) Full Text: DOI
Yamagishi, Hiroyuki; Watanabe, Kohtaro The best constant of \(L^p\) Sobolev inequality including \(j\)-th derivative corresponding to periodic and Neumann boundary value problem for \((-1)^M(d/dx)^{2M}\). (English) Zbl 1311.34044 Tokyo J. Math. 37, No. 2, 485-501 (2014). MSC: 34B15 34B27 46E35 PDFBibTeX XMLCite \textit{H. Yamagishi} and \textit{K. Watanabe}, Tokyo J. Math. 37, No. 2, 485--501 (2014; Zbl 1311.34044) Full Text: DOI Euclid
Yamagishi, Hiroyuki; Watanabe, Kohtaro; Kametaka, Yoshinori The best constant of \(L^p\) Sobolev inequality corresponding to Dirichlet-Neumann boundary value problem. (English) Zbl 1302.34033 Math. J. Okayama Univ. 56, 145-155 (2014). Reviewer: Petr Necesal (Plzen) MSC: 34B05 34B27 46E35 PDFBibTeX XMLCite \textit{H. Yamagishi} et al., Math. J. Okayama Univ. 56, 145--155 (2014; Zbl 1302.34033)
Takemura, Kazuo; Kametaka, Yoshinori; Watanabe, Kohtaro; Nagai, Atsushi; Yamagishi, Hiroyuki Sobolev type inequalities of time-periodic boundary value problems for Heaviside and Thomson cables. (English) Zbl 1282.46035 Bound. Value Probl. 2012, Paper No. 95, 15 p. (2012). MSC: 46E35 41A44 34B27 PDFBibTeX XMLCite \textit{K. Takemura} et al., Bound. Value Probl. 2012, Paper No. 95, 15 p. (2012; Zbl 1282.46035) Full Text: DOI
Yamagishi, Hiroyuki; Kametaka, Yoshinori; Nagai, Atsushi; Watanabe, Kohtaro; Takemura, Kazuo Elliptic theta function and the best constants of Sobolev-type inequalities. (English) Zbl 1273.26028 JSIAM Lett. 4, 1-4 (2012). MSC: 26D10 26D15 PDFBibTeX XMLCite \textit{H. Yamagishi} et al., JSIAM Lett. 4, 1--4 (2012; Zbl 1273.26028) Full Text: DOI Link
Kametaka, Yoshinori; Takemura, Kazuo; Yamagishi, Hiroyuki; Nagai, Atsushi; Watanabe, Kohtaro Positivity and hierarchical structure of 16 Green functions corresponding to a bending problem of a beam. (English) Zbl 1264.34049 Saitama Math. J. 29, 1-24 (2012). MSC: 34B27 34B05 PDFBibTeX XMLCite \textit{Y. Kametaka} et al., Saitama Math. J. 29, 1--24 (2012; Zbl 1264.34049)
Oshime, Yorimasa; Yamagishi, Hiroyuki; Watanabe, Kohtaro The best constant of \(L^p\) Sobolev inequality corresponding to Neumann boundary value problem for \((-1)^M(d/dx)^{2M}\). (English) Zbl 1262.34028 Hiroshima Math. J. 42, No. 3, 293-299 (2012). MSC: 34B15 34B27 46E35 PDFBibTeX XMLCite \textit{Y. Oshime} et al., Hiroshima Math. J. 42, No. 3, 293--299 (2012; Zbl 1262.34028) Full Text: Euclid
Watanabe, Kohtaro; Yamagishi, Hiroyuki; Kametaka, Yoshinori Riemann zeta function and Lyapunov-type inequalities for certain higher order differential equations. (English) Zbl 1254.34027 Appl. Math. Comput. 218, No. 7, 3950-3953 (2011). Reviewer: Antonio Cañada Villar (Granada) MSC: 34B05 34B27 PDFBibTeX XMLCite \textit{K. Watanabe} et al., Appl. Math. Comput. 218, No. 7, 3950--3953 (2011; Zbl 1254.34027) Full Text: DOI
Takemura, Kazuo; Kametaka, Yoshinori; Watanabe, Kohtaro; Nagai, Atsushi; Yamagishi, Hiroyuki The best constant of Sobolev inequality corresponding to a bending problem of a beam on a half line. (English) Zbl 1232.34041 Far East J. Appl. Math. 51, No. 1, 45-71 (2011). Reviewer: Abdelghani Ouahab (Sidi Bel Abbes) MSC: 34B27 34B15 34B40 46E22 PDFBibTeX XMLCite \textit{K. Takemura} et al., Far East J. Appl. Math. 51, No. 1, 45--71 (2011; Zbl 1232.34041) Full Text: Link
Watanabe, Kohtaro; Kametaka, Yoshinori; Yamagishi, Hiroyuki; Nagai, Atsushi; Takemura, Kazuo The best constant of Sobolev inequality corresponding to clamped boundary value problem. (English) Zbl 1221.46036 Bound. Value Probl. 2011, Article ID 875057, 17 p. (2011). MSC: 46E35 34B27 26D10 26D15 PDFBibTeX XMLCite \textit{K. Watanabe} et al., Bound. Value Probl. 2011, Article ID 875057, 17 p. (2011; Zbl 1221.46036) Full Text: DOI EuDML
Yamagishi, Hiroyuki; Kametaka, Yoshinori; Nagai, Atsushi; Watanabe, Kohtaro; Takemura, Kazuo Riemann zeta function and the best constants of five series of Sobolev inequalities. (English) Zbl 1232.34042 RIMS Kôkyûroku Bessatsu B13, 125-139 (2009). Reviewer: Alberto Cabada (Santiago de Compostela) MSC: 34B27 34B15 PDFBibTeX XMLCite \textit{H. Yamagishi} et al., RIMS Kôkyûroku Bessatsu B13, 125--139 (2009; Zbl 1232.34042)
Kametaka, Yoshinori; Nagai, Atsushi; Takemura, Kazuo; Watanabe, Kohtaro; Yamagishi, Hiroyuki The best constant of Sobolev inequality corresponding to a bending problem of a beam on an interval. (English) Zbl 1209.34016 Tsukuba J. Math. 33, No. 2, 253-280 (2009). Reviewer: Antonio Linero Bas (Murcia) MSC: 34B05 34B27 46E35 41A44 PDFBibTeX XMLCite \textit{Y. Kametaka} et al., Tsukuba J. Math. 33, No. 2, 253--280 (2009; Zbl 1209.34016) Full Text: DOI Euclid
Kametaka, Yoshinori; Oshime, Yorimasa; Watanabe, Kohtaro; Yamagishi, Hiroyuki; Nagai, Atsushi; Takemura, Kazuo The best constant of \(L^p\) Sobolev inequality corresponding to the periodic boundary value problem for \((-1)^M(d/dx)^{2M}\). (English) Zbl 1168.46018 Sci. Math. Jpn. 66, No. 2, 169-181 (2007). Reviewer: Fabrice Colin (Sudbury) MSC: 46E35 41A44 34B27 PDFBibTeX XMLCite \textit{Y. Kametaka} et al., Sci. Math. Jpn. 66, No. 2, 169--181 (2007; Zbl 1168.46018)
Kametaka, Yoshinori; Watanabe, Kohtaro; Nagai, Atsushi; Yamagishi, Hiroyuki; Takemura, Kazuo The best constant of Sobolev inequality which corresponds to a bending problem of a string with periodic boundary condition. (English) Zbl 1173.46016 Sci. Math. Jpn. 66, No. 2, 151-168 (2007). Reviewer: Fabrice Colin (Sudbury) MSC: 46E35 34B27 41A44 PDFBibTeX XMLCite \textit{Y. Kametaka} et al., Sci. Math. Jpn. 66, No. 2, 151--168 (2007; Zbl 1173.46016)
Watanabe, Kohtaro; Yamada, Takeo; Takahashi, Wataru Reproducing kernels of \(H^m (a,b)\) \((m= 1,2,3)\) and least constants in Sobolev’s inequalities. (English) Zbl 1051.46021 Appl. Anal. 82, No. 8, 809-820 (2003). Reviewer: Bohumír Opic (Praha) MSC: 46E35 34B27 PDFBibTeX XMLCite \textit{K. Watanabe} et al., Appl. Anal. 82, No. 8, 809--820 (2003; Zbl 1051.46021) Full Text: DOI