A Functional Analytic Perspective to the div-curl Lemma

Marcus Waurick

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arXiv · 1703.09593

A Functional Analytic Perspective to the div-curl Lemma

Marcus Waurick

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Abstract

We present an abstract functional analytic formulation of the celebrated $\dive$-$\curl$ 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 $\Grad\grad$-sequence discovered recently by D.~Pauly and W.~Zulehner in connection with the biharmonic operator.

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Marcus Waurick. 2017-03-28. A Functional Analytic Perspective to the div-curl Lemma. https://arxiv.org/abs/1703.09593

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