Balls have the worst best Sobolev inequalities. II: Variants and extensions

DOI10.1007/s00526-007-0105-xzbMath1135.46016OpenAlexW2081060500MaRDI QIDQ2462261

Francesco Maggi, Cédric Villani

Publication date: 28 November 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-007-0105-x

zbMATH Keywords

logarithmic Sobolev inequalitiesSobolev inequalitiesGagliardo-Nirenberg inequalitiesMoser-Trudinger inequalitiesFaber-Krahn inequalitiesmass transport methods

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Partial differential inequalities and systems of partial differential inequalities (35R45) Inequalities for sums, series and integrals (26D15)

Related Items (15)

A bridge between Sobolev and Escobar inequalities and beyond ⋮ A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients ⋮ Poincaré trace inequalities in \(BV({\mathbb {B}}^n)\) with non-standard normalization ⋮ Balls minimize trace constants in BV ⋮ A survey on dynamical transport distances ⋮ A dual Moser-Onofri inequality and its extensions to higher dimensional spheres ⋮ Balls have the worst best Sobolev inequalities ⋮ Friedrichs-type inequalities in arbitrary domains ⋮ Sobolev inequalities for the symmetric gradient in arbitrary domains ⋮ A Note on Some Poincaré Inequalities on Convex Sets by Optimal Transport Methods ⋮ Sharp trace inequalities for fractional Laplacians ⋮ Best constant in Poincaré inequalities with traces: a free discontinuity approach ⋮ Sharp weighted Sobolev and Gagliardo–Nirenberg inequalities on half-spaces via mass transport and consequences ⋮ Uniform Poincaré-Sobolev and isoperimetric inequalities for classes of domains ⋮ Sobolev inequalities in arbitrary domains

Cites Work

• Contributions to the theory of convex bodies
• Best constant in Sobolev trace inequalities on the half-space
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
• Blocking of billiard orbits and security for polygons and flat surfaces
• Optimal Transport
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