Symmetrization of functions and the best constant of 1-dim \(L^p\) Sobolev inequality

DOI10.1155/2009/874631zbMath1191.46031OpenAlexW2156279234WikidataQ59219769 ScholiaQ59219769MaRDI QIDQ962455

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

Publication date: 7 April 2010

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/232519

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (6)

Chebyshev-type polynomials arising in Poincaré limit inequalities ⋮ Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator ⋮ 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 ⋮ The best constant of \(L^p\) Sobolev inequality corresponding to Dirichlet boundary value problem. II ⋮ 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

• 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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