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

DOI10.32917/hmj/1355238370zbMath1262.34028OpenAlexW1520465626MaRDI QIDQ1940032

Hiroyuki Yamagishi, Yorimasa Oshime, Kohtaro Watanabe

Publication date: 5 March 2013

Published in: Hiroshima Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.hmj/1355238370

zbMATH Keywords

reproducing kernelGreen functionHölder inequalityBernoulli polynomialbest constant\(L^p\) Sobolev inequality

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Green's functions for ordinary differential equations (34B27)

Related Items (2)

Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains ⋮ 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

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• The best constant of Sobolev inequality corresponding to clamped boundary value problem
• The best constant of \(L^p\) Sobolev inequality corresponding to Dirichlet boundary value problem. II
• Symmetrization of functions and the best constant of 1-dim \(L^p\) Sobolev inequality

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