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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DOI:
http://dx.doi.org/10.1090/S0002-9947-1987-0902788-8

Article copyright:
© Copyright 1987
American Mathematical Society