New estimates for elliptic equations and Hodge type systems
Jean Bourgain
Institute for Advanced Study, Princeton, United StatesHaïm Brezis
Rutgers University, Piscataway, United States
Abstract
We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimensionn, with data inL1. We also present related results concerning differential forms with coefficients in the limiting Sobolev spaceW1,n.
Cite this article
Jean Bourgain, Haïm Brezis, New estimates for elliptic equations and Hodge type systems. J. Eur. Math. Soc. 9 (2007), no. 2, pp. 277–315
DOI 10.4171/JEMS/80Dates
- Submitted
- 6 August 2006
- Published
- 30 June 2007
Identifiers
Keywords
- Elliptic systems
- data in <em>L<sup>1</sup></em>
- div-curl
- Hodge systems
- limiting Sobolev spaces
- differential forms
- Littlewood–Paley decomposition
- Ginzburg–Landau functional
Mathematics Subject Classification
- 35-XX
- 42-XX
- 46-XX
- 58-XX