On the constants for some fractional Gagliardo-Nirenberg and Sobolev inequalities

DOI10.1016/j.exmath.2017.08.007zbMath1396.46030arXiv1611.00734OpenAlexW3104160814MaRDI QIDQ1747827

Carlo Morosi, Livio Pizzocchero

Publication date: 27 April 2018

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00734

zbMATH Keywords

Sobolev inequalityfractional Gagliardo-Nirenberg inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fractional derivatives and integrals (26A33) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (17)

Large deviation principle for occupation measures of two dimensional stochastic convective Brinkman-Forchheimer equations ⋮ Remarks on the damped nonlinear Schrödinger equation ⋮ Finite fractal dimension of random attractors for non-autonomous fractional stochastic reaction–diffusion equations in ℝ ⋮ Dynamics of fractional nonclassical diffusion equations with delay driven by additive noise on \(\mathbb{R}^n\) ⋮ Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise ⋮ Large deviation principle for occupation measures of stochastic generalized Burgers-Huxley equation ⋮ On coupled nonlinear Schrödinger systems ⋮ Long-time dynamics of fractional nonclassical diffusion equations with nonlinear colored noise and delay on unbounded domains ⋮ Standing waves of the quintic NLS equation on the tadpole graph ⋮ Upper semi-continuity of attractors for non-autonomous fractional stochastic parabolic equations with delay ⋮ Bi-spatial pullback attractors of fractional nonclassical diffusion equations on unbounded domains with \((p, q)\)-growth nonlinearities ⋮ Controllability of the Navier-Stokes equation in a rectangle with a little help of a distributed phantom force ⋮ Unexpected quadratic behaviors for the small-time local null controllability of scalar-input parabolic equations ⋮ Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one ⋮ Asymptotic behavior of fractional nonclassical diffusion equations driven by nonlinear colored noise on $\mathbb{R}^N$ ⋮ Existence of attractors for stochastic diffusion equations with fractional damping and time-varying delay ⋮ A Gagliardo-Nirenberg type inequality for rapidly decaying functions

Uses Software

• DLMF

Cites Work

• Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms
• Theory of Bessel potentials. I
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Gaussian kernels have only Gaussian maximizers
• Gagliardo-Nirenberg inequalities involving the gradient \(L^2\)-norm
• Best constant in Sobolev inequality
• Problèmes isoperimetriques et espaces de Sobolev
• On the constants for some Sobolev imbeddings.
• Sharp Sobolev type inequalities for higher fractional derivatives
• Best constants for Sobolev inequalities for higher order fractional derivatives
• The special functions and their approximations. Vol. I, II
• Ulteriori proprieta di alcune classi di funzioni in piu variabili
• Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators
• Best Constants in Sobolev Inequalities on the Sphere and in Euclidean Space
• Classical Fourier Analysis
• Modern Fourier Analysis
• Solutions of certain fractional kinetic equations and a fractional diffusion equation
• Fourier Transforms. (AM-19)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the constants for some fractional Gagliardo-Nirenberg and Sobolev inequalities