Reproducing Kernels ofHm(a, b) (m= 1, 2, 3) and Least Constants in Sobolev’s Inequalities

DOI10.1080/0003681031000152541zbMath1051.46021OpenAlexW2094746312WikidataQ58264428 ScholiaQ58264428MaRDI QIDQ4459847

Takahashi, Wataru, Kohtaro Watanabe, Takeo Yamada

Publication date: 18 May 2004

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/0003681031000152541

zbMATH Keywords

reproducing kernelGreen functionSobolev embeddingleast constant

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Green's functions for ordinary differential equations (34B27)

Related Items (7)

Global existence and blow-up of solutions for a nonlinear wave equation with memory ⋮ The reproducing Kernel of the Sobolev space on an interval ⋮ Periodic traveling wave solutions of discrete nonlinear Klein‐Gordon lattices ⋮ Reproducing kernels of Sobolev spaces on ℝd and applications to embedding constants and tractability ⋮ 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 Sobolev inequality in an \(n\)-dimensional Euclidean space

Cites Work

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• Functional analysis, Sobolev spaces and partial differential equations
• Best constant in Sobolev inequality
• Evaluation of the Least Constant in Sobolev’s Inequality for $H^1 (0,s)$

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