New estimates for the div-curl-grad operators and elliptic problems with \(L^{1}\)-data in the whole space and in the half-space

DOI10.1016/j.jde.2011.01.012zbMath1213.35205OpenAlexW2009763231MaRDI QIDQ630586

Chérif Amrouche, Nguyen Huy Hoang

Publication date: 17 March 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.01.012

zbMATH Keywords

weighted Sobolev spacesDirichlet boundary conditionsNeumann boundary conditionselliptic systemdiv-curl-grad operators

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30) Second-order elliptic systems (35J47) Boundary value problems for second-order elliptic systems (35J57)

Related Items (5)

\(L^{3/2}\)-estimates of vector fields with \(L^{1}\) curl in a bounded domain ⋮ Approximation in higher-order Sobolev spaces and Hodge systems ⋮ A subelliptic Bourgain-Brezis inequality ⋮ Asymptotic global fast dynamics and attractor fractal dimension of the TDGL-equations of superconductivity ⋮ Limiting Bourgain-Brezis estimates for systems of linear differential equations: theme and variations

Cites Work

• The Neumann problem in the half-space
• Note on a lemma of Finn and Gilbar
• New estimates for elliptic equations and Hodge type systems
• Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces
• On the equation \(\text{div }u=f\)
• New estimates for the Laplacian, the div-curl, and related Hodge systems
• Estimates for \(L^{1}\)-vector fields
• Weighted Sobolev spaces for Laplace's equation in \(\mathbb{R}^ n\)
• Very weak, generalized and strong solutions to the Stokes system in the half-space
• Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace
• Boundary estimates for elliptic systems with \(L^{1}\)- data
• The stationary Oseen equations in \({\mathbb{R}}^{3}\). An approach in weighted Sobolev spaces
• Les espaces du type de Beppo Levi
• Laplace equation in the half-space with a nonhomogeneous Dirichlet boundary condition
• HARDY SPACES OF SOLENOIDAL VECTOR FIELDS, WITH APPLICATIONS TO THE NAVIER-STOKES EQUATIONS
• THE STOKES PROBLEM IN ℝⁿ: AN APPROACH IN WEIGHTED SOBOLEV SPACES
• On the equation 𝑑𝑖𝑣𝑌=𝑓 and application to control of phases
• From Strong to Very Weak Solutions to the Stokes System with Navier Boundary Conditions in the Half-Space
• Equivalent Norms for Sobolev Spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: New estimates for the div-curl-grad operators and elliptic problems with \(L^{1}\)-data in the whole space and in the half-space