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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On weak continuity and the Hodge decomposition
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by Joel W. Robbin, Robert C. Rogers and Blake Temple PDF
Trans. Amer. Math. Soc. 303 (1987), 609-618 Request permission

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.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 303 (1987), 609-618
  • MSC: Primary 58A14; Secondary 35A30, 58C07, 58G30
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0902788-8
  • MathSciNet review: 902788