Sharp constants in the Sobolev embedding theorem and a derivation of the Brezis-Gallouet interpolation inequality

DOI10.1063/1.3638056zbMath1272.46020OpenAlexW2134174621MaRDI QIDQ2849755

Michele V. Bartuccelli, John D. Gibbon

Publication date: 24 September 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://epubs.surrey.ac.uk/806738/1/BG-JMP-2011.pdf

zbMATH Keywords

Riemann zeta-functionDirichlet beta-series

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Interpolation in approximation theory (41A05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
• Nonlinear Schrödinger equations and sharp interpolation estimates
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Sobolev inequalities with remainder terms
• On the constants for some Sobolev imbeddings.
• Asymptotic estimates for Gagliardo-Nirenberg embedding constants
• Length scales for the Navier-Stokes equations on a rotating sphere
• Double logarithmic inequality with a sharp constant
• An optimal limiting 2𝐷 Sobolev inequality
• Nonlinear Schrödinger evolution equations
• On two inequalities of sobolev type
• Exact values of some two-dimensional lattice sums
• Positivity and the attractor dimension in a fourth-order reaction-diffusion equation
• Best Constants in Multiplicative Inequalities for Sup-Norms
• Applied Analysis of the Navier-Stokes Equations
• Lieb-Thirring integral inequalities and their applications to attractors of the Navier-Stokes equations

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