Limiting Bourgain-Brezis estimates for systems: theme and variations

Abstract

J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case ${\mathrm{L}}^1$ of singular integral estimates and the critical Sobolev space ${\mathrm{W}}^{1,n}({\mathbf{R}}^n)$. This paper presents an overview of the results, further developments over the last ten years and challenging open problems.

arXiv comment22 pages, minor typos corrected and references updated

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Cited by in corpus (7)

• A guide to the Choquard equation
• Ground state solutions for non-autonomous fractional Choquard equations
• Standing waves with a critical frequency for nonlinear Choquard equations
• Multiple and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent
• Nonlinear Perturbations of a periodic magnetic Choquard equation with Hardy-Littlewood-Sobolev critical exponent
• Concentration Behavior of Nonlinear Hartree-type Equation with almost Mass Critical Exponent
• Nonstandard solutions for a perturbed nonlinear Schrödinger system with small coupling coefficients\protect\thanks{A perturbed nonlinear Schrödinger system