The best constant of \(L^p\) Sobolev inequality including \(j\)-th derivative corresponding to periodic and Neumann boundary value problem for \((-1)^M(d/dx)^{2M}\)
DOI10.3836/tjm/1422452804zbMath1311.34044OpenAlexW2058588270MaRDI QIDQ2339634
Hiroyuki Yamagishi, Kohtaro Watanabe
Publication date: 2 April 2015
Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.tjm/1422452804
reproducing kernelGreen functionHölder inequalityBernoulli polynomialbest constant\(L^p\) Sobolev inequality
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)
Cites Work
- Lyapunov-type inequalities for \(2M\)th order equations under clamped-free boundary conditions
- 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
- 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 corresponding to Neumann boundary value problem for \((-1)^M(d/dx)^{2M}\)
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