A Functional Analytic Perspective to the div-curl Lemma

Autor: Waurick, Marcus
Rok vydání: 2017
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Comment: 18 pages; some typos removed, Remark 2.3 added, Proposition 3.10 clarified
Databáze: arXiv