New estimates for elliptic equations and Hodge type systems.(English)Zbl 1176.35061
In this paper the authors establish new and important estimates for the Laplace operator, the div-curl system, and more general Hodge systems in arbitrary dimensions \(n\), with data in \(L^1\). They also present related results concerning differential forms with coefficients in the limiting Sobolev space \(W^{1,n}\). The proofs rely essentially on the Littlewood-Paley theory combined with refined analytic estimates.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 35J48 | Higher-order elliptic systems |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 58A10 | Differential forms in global analysis |
Keywords:
elliptic system;data in \(L^1\);div-curl;Hodge system;limiting Sobolev spaces;differential form;Littlewood-Paley decomposition;Ginzburg-Landau functionalCite
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