72 research outputs found
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
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