Geodesic
New estimates for elliptic equations and Hodge type systems
Journal of the European Mathematical Society, Tome 9 (2007) no. 2, pp. 277-315

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We establish new estimates for the Laplacian, the div-curl system, and more general Hodge systems in arbitrary dimension n, with data in L1. We also present related results concerning differential forms with coefficients in the limiting Sobolev space W1,n.
DOI : 10.4171/jems/80
Classification : 35-XX, 42-XX, 46-XX, 58-XX
Keywords: Elliptic systems, data in L1, div-curl, Hodge systems, limiting Sobolev spaces, differential forms, Littlewood–Paley decomposition, Ginzburg–Landau functional 
@article{JEMS_2007_9_2_a3,
     author = {Jean Bourgain and Ha{\"\i}m Brezis},
     title = {New estimates for elliptic equations and {Hodge} type systems},
     journal = {Journal of the European Mathematical Society},
     pages = {277--315},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2007},
     doi = {10.4171/jems/80},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/80/}
}
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Jean Bourgain; Haïm Brezis. New estimates for elliptic equations and Hodge type systems. Journal of the European Mathematical Society, Tome 9 (2007) no. 2, pp. 277-315. doi: 10.4171/jems/80

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