The best constant of \(L^p\) Sobolev inequality corresponding to Dirichlet boundary value problem. II

DOI10.3836/tjm/1313074446zbMath1237.34028OpenAlexW2081246755MaRDI QIDQ719099

Yorimasa Oshime, Kohtaro Watanabe

Publication date: 27 September 2011

Published in: Tokyo Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3836/tjm/1313074446

zbMATH Keywords

symmetrizationDirichlet boundary conditionSobolev inequalitybest constant

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 (4)

Sharp constants for inequalities of Poincaré type: an application of optimal control theory ⋮ 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 \((-1)^M(d/dx)^{2M}\) ⋮ 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

• Symmetrization of functions and the best constant of 1-dim \(L^p\) Sobolev inequality
• The best constant of Sobolev inequality on a bounded interval
• Sharp constants in inequalities for intermediate derivatives (the Gabushin case)
• Steepest Descent and the Least C for Sobolev's Inequality
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