Journal of Operator Theory

Volume 80, Issue 1, Summer 2018 pp. 95-111.

A functional analytic perspective to the div-curl lemma

Authors: Marcus Waurick
Author institution: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, Scotland, U.K.

Summary: We present an abstract functional analytic formulation of the celebrated div-curl lemma found by F. Murat and L. Tartar. The viewpoint in this note relies on sequences for operators in Hilbert spaces. Hence, we draw the functional analytic relation of the div-curl lemma to differential forms and other sequences such as the $\mathrm{Grad\,}\mathrm{grad}$-sequence discovered recently by D. Pauly and W. Zulehner in connection with the biharmonic operator.

DOI: http://dx.doi.org/10.7900/jot.2017jun09.2154
Keywords: div-curl lemma, compensated compactness, de Rham complex

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