Abstract
In this paper we give an affirmative answer to the Euclidean analogue of a question of Bourgain and Brezis concerning the optimal Lorentz estimate for a Div–Curl system: If F∈L1(R3;R3) satisfies divF=0 in the sense of distributions, then the function Z=curl(-Δ)-1F satisfies (Formula presented.) and there exists a constant C>0 such that (Formula presented.) Our proof relies on a new endpoint Hardy–Littlewood–Sobolev inequality for divergence free measures which we obtain via a result of independent interest, an atomic decomposition of such objects.
Original language | English |
---|---|
Article number | 117 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 63 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2024 Jun |
Keywords
- 31B10
- 35J46
- 46E35
ASJC Scopus subject areas
- Analysis
- Applied Mathematics