Estimates for \(L^{1}\)-vector fields under higher-order differential conditions

DOI10.4171/JEMS/133zbMath1228.46034OpenAlexW2027365306MaRDI QIDQ952508

Jean Van Schaftingen

Publication date: 12 November 2008

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=10&iss=4&rank=1

zbMATH Keywords

Schrödinger equationsSobolev inequalitycompensationcritical Sobolev spaces\(L^{2}\)-critical NLSKorn-Sobolev inequalitypseudo-conformal blow-up

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities for sums, series and integrals (26D15)

Related Items (18)

Weakly canceling operators and singular integrals ⋮ Gagliardo-Nirenberg inequalities for differential forms in Heisenberg groups ⋮ A note on an inequality of Bourgain and Brezis ⋮ Limiting Sobolev and Hardy inequalities on stratified homogeneous groups ⋮ On the complex constant rank condition and inequalities for differential operators ⋮ Boundary ellipticity and limiting \(\mathrm{L}^1\)-estimates on halfspaces ⋮ Endpoint \(L^1\) estimates for Hodge systems ⋮ Sharp a priori estimates for div-curl systems in Heisenberg groups ⋮ Approximation in higher-order Sobolev spaces and Hodge systems ⋮ A subelliptic Bourgain-Brezis inequality ⋮ Continuity and canceling operators of order \(n\) on \(\mathbb{R}^n\) ⋮ Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations ⋮ Local $\mathbf {L}^{1}$ estimates for elliptic systems of complex vector fields ⋮ L1 Sobolev estimates for (pseudo)-differential operators and applications ⋮ Limiting fractional and Lorentz space estimates of differential forms ⋮ Estimate of the pressure when its gradient is the divergence of a measure. Applications ⋮ Embeddings for \(\mathbb{A}\)-weakly differentiable functions on domains ⋮ Bourgain-Brezis inequalities on symmetric spaces of non-compact type

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• New estimates for elliptic equations and Hodge type systems
• A simple proof of an inequality of Bourgain, Brezis and Mironescu.
• A note on div curl inequalities
• New estimates for the Laplacian, the div-curl, and related Hodge systems
• Estimates for \(L^{1}\)-vector fields
• \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation
• On the equation 𝑑𝑖𝑣𝑌=𝑓 and application to control of phases

This page was built for publication: Estimates for \(L^{1}\)-vector fields under higher-order differential conditions