The best constant of Sobolev inequality corresponding to clamped boundary value problem

DOI10.1155/2011/875057zbMath1221.46036OpenAlexW4234864005MaRDI QIDQ536836

Atsushi Nagai, Kohtaro Watanabe, Hiroyuki Yamagishi, Yoshinori Kametaka, Kazuo Takemura

Publication date: 19 May 2011

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/224615

zbMATH Keywords

Green's functionSobolev inequalitybest constantclamped boundary value problem

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) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (8)

New Lyapunov-type inequalities for a class of even-order linear differential equations ⋮ On multivariate higher order Lyapunov-type inequalities ⋮ Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains ⋮ The best constant of \(L^p\) Sobolev inequality corresponding to Neumann boundary value problem for \((-1)^M(d/dx)^{2M}\) ⋮ On the symmetry of extremal in several embedding theorems ⋮ Lyapunov-type inequalities for higher order half-linear differential equations ⋮ Factorization of the Green's operator in the Dirichlet problem for \((-1)^m(d/dt)^{2m}\) ⋮ 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

• Green's function for n-n boundary value problem and an analogue of Hartman's result
• On inequalities of Lyapunov type
• A generalized Liapunov inequality
• Eigenvalues of a Sturm-Liouville problem and inequalities of Lyapunov type

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