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.

22 pages, minor typos corrected and references updated

References in corpus (2)

• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains

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