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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On weak continuity and the Hodge decomposition

Authors: Joel W. Robbin, Robert C. Rogers and Blake Temple
Journal: Trans. Amer. Math. Soc. 303 (1987), 609-618
MSC: Primary 58A14; Secondary 35A30, 58C07, 58G30
MathSciNet review: 902788
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Abstract: We address the problem of determining the weakly continuous polynomials for sequences of functions that satisfy general linear first-order differential constraints. We prove that wedge products are weakly continuous when the differential constraints are given by exterior derivatives. This is sufficient for reproducing the Div-Curl Lemma of Murat and Tartar, the null Lagrangians in the calculus of variations and the weakly continuous polynomials for Maxwell’s equations. This result was derived independently by Tartar who stated it in a recent survey article [7]. Our proof is explicit and uses the Hodge decomposition.

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Article copyright: © Copyright 1987 American Mathematical Society