The best constant of Sobolev inequality corresponding to clamped-free boundary value problem for \((-1)^M(d/dx)^{2M}\)

DOI10.3792/pjaa.85.112zbMath1206.34048OpenAlexW1976607204MaRDI QIDQ1046451

Kazuo Takemura

Publication date: 22 December 2009

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.85.112

zbMATH Keywords

reproducing kernelGreen functionSobolev inequalitybest constantLU decomposition

Mathematics Subject Classification ID

Green's functions for ordinary differential equations (34B27) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Linear boundary value problems for ordinary differential equations (34B05) Best constants in approximation theory (41A44)

Related Items

Lyapunov-type inequalities for \(2M\)th order equations under clamped-free boundary conditions, Sobolev inequality of free boundary value problem for \((-1)^{M}(d/dx)^{2M}\), The best constant of Sobolev inequality corresponding to clamped-free boundary value problem for \((-1)^M(d/dx)^{2M}\), The best constant of \(L^p\) Sobolev inequality including \(j\)-th derivative corresponding to periodic and Neumann boundary value problem for \((-1)^M(d/dx)^{2M}\)

Cites Work

• The best constant of Sobolev inequality in an \(n\)-dimensional Euclidean space
• The best constant of Sobolev inequality corresponding to clamped-free boundary value problem for \((-1)^M(d/dx)^{2M}\)
• Best constant in Sobolev inequality
• Reproducing Kernels ofH^m(a, b) (m= 1, 2, 3) and Least Constants in Sobolev’s Inequalities
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