Partial Differential Equations
New estimates for the Laplacian, the div–curl, and related Hodge systems

Presented by: Haïm Brezis

Bourgain, Jean1; Brezis, Haïm2, 3
1 Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA
2 Analyse numérique, Université P. et M. Curie, BC 187, 4, place Jussieu, 75252 Paris cedex 05, France
3 Department of Mathematics, Rutgers University, Hill Center, Busch Campus, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA
Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 539-543.

We establish new estimates for the Laplacian, the div–curl system, and more general Hodge systems in arbitrary dimension, with an application to minimizers of the Ginzburg–Landau energy.

On établit de nouvelles estimées pour le Laplacien, le système div–rot et autres systèmes de Hodge en dimension quelconque. On présente une application aux minimiseurs de l'énergie de Ginzburg–Landau.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.12.031
Bourgain, Jean 1; Brezis, Haïm 2, 3

1 Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA
2 Analyse numérique, Université P. et M. Curie, BC 187, 4, place Jussieu, 75252 Paris cedex 05, France
3 Department of Mathematics, Rutgers University, Hill Center, Busch Campus, 110, Frelinghuysen Road, Piscataway, NJ 08854, USA 
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Bourgain, Jean; Brezis, Haïm. New estimates for the Laplacian, the div–curl, and related Hodge systems. Comptes Rendus. Mathématique, Volume 338 (2004) no. 7, pp. 539-543. doi : 10.1016/j.crma.2003.12.031. http://archive.numdam.org/articles/10.1016/j.crma.2003.12.031/

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