A Functional Analytic Perspective to the div-curl Lemma

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 clarifie

On the homogenization of partial integro-differential-algebraic equations

We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics, elasticity, electro-magnetism and coupled systems thereof. The approach permits the consideration of memory problems as well as differential-algebraic equations. We show that the limit equation is well-posed and causal. We rely on techniques from functional analysis and operator theory only.Comment: Thoroughly revised, changed title, reviewer's comments incorporated, added some references. 41 page