Detailed proof of classical Gagliardo-Nirenberg interpolation inequality with historical remarks

DOI10.4171/ZAA/1681zbMath1479.46038arXiv1812.04281OpenAlexW3149925149WikidataQ112842152 ScholiaQ112842152MaRDI QIDQ2039398

Filip Soudský, Alberto Fiorenza, Maria Rosaria Formica, Tomáš G. Roskovec

Publication date: 2 July 2021

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.04281

zbMATH Keywords

Sobolev spacesSobolev embedding theoreminequalities for derivativesGagliardo-Nirenberg inequalityinterpolation inequalityintermediate derivatives

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) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (12)

Short proofs for interpolation inequalities in Sobolev spaces with variable exponents ⋮ Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications ⋮ Global in time solution to Kolmogorov's two-equation model of turbulence with small initial data ⋮ Fractional Gagliardo-Nirenberg interpolation inequality and bounded mean oscillation ⋮ Optimal Gagliardo-Nirenberg interpolation inequality for rearrangement invariant spaces ⋮ Regularity of the inverse mapping in Banach function spaces ⋮ Weighted Gagliardo-Nirenberg interpolation inequalities ⋮ On symmetry of energy minimizing harmonic-type maps on cylindrical surfaces ⋮ A short proof of the Gagliardo-Nirenberg inequality with BMO term ⋮ Gagliardo-Nirenberg inequality for rearrangement-invariant Banach function spaces ⋮ On the regularity of solutions to a class of degenerate PDE's with lower order terms ⋮ An efficient and accurate numerical scheme for long time statistical properties of the infinite Prandtl number model for convection

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