A functional analytic perspective to the div-curl Lemma

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Abstract

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 Grad grad-sequence discovered recently by D. Pauly and W. Zulehner in connection with the biharmonic operator.
Original languageEnglish
Number of pages18
JournalJournal of Operator Theory
Publication statusAccepted/In press - 6 Jul 2017

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Curl
Lemma
Biharmonic Operator
Differential Forms
Hilbert space
Formulation
Operator

Keywords

  • div-curl lemma
  • compensated compactness
  • de Rham complex

Cite this

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A functional analytic perspective to the div-curl Lemma. / Waurick, Marcus.

In: Journal of Operator Theory, 06.07.2017.

Research output: Contribution to journalArticle

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