On some inequalities of Bourgain, Brezis, Maz'ya, and Shaposhnikova related to \(L^1\) vector fields

DOI10.1016/j.crma.2010.03.019zbMath1204.35082OpenAlexW2044630309MaRDI QIDQ974012

Petru Mironescu

Publication date: 26 May 2010

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2010.03.019

zbMATH Keywords

biharmonic operatorBourgain-Brezis approachMaz'ya approach

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Inequalities involving derivatives and differential and integral operators (26D10) Higher-order elliptic equations (35J30)

Related Items (7)

An optimal Sobolev embedding for \(L^1\) ⋮ A limiting case for the divergence equation ⋮ Approximation in higher-order Sobolev spaces and Hodge systems ⋮ A subelliptic Bourgain-Brezis inequality ⋮ Bergman-Bourgain-Brezis-type inequality ⋮ Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations ⋮ Hierarchical Construction of Bounded Solutions in Critical Regularity Spaces

Cites Work

• Estimates for differential operators of vecor analysis involving \(L^{1}\)-norm
• New estimates for elliptic equations and Hodge type systems
• New estimates for the Laplacian, the div-curl, and related Hodge systems
• A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions
• On the equation 𝑑𝑖𝑣𝑌=𝑓 and application to control of phases
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