Journal of the European Mathematical Society

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Volume 9, Issue 2, 2007, pp. 277–315
DOI: 10.4171/JEMS/80

New estimates for elliptic equations and Hodge type systems

Jean Bourgain[1] and Haïm Brezis[2]

(1) School of Mathematics, Institute for Advanced Study, 1 Einstein Drive, NJ 08540, Princeton, USA
(2) Department of Mathematics, Rutgers University, Hill Center, Busch Campus, 110 Frelinghuysen Road, NJ 08854, Piscataway, USA

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.

Keywords: Elliptic systems, data in L1, div-curl, Hodge systems, limiting Sobolev spaces, differential forms, Littlewood–Paley decomposition, Ginzburg–Landau functional

Bourgain Jean, Brezis Haïm: New estimates for elliptic equations and Hodge type systems. J. Eur. Math. Soc. 9 (2007), 277-315. doi: 10.4171/JEMS/80