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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