Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogenisation and the Weak Operator Topology   This article surveys results that relate homogenisation problems for partial
differential equations and convergence in the weak operator topology of a
suitable choice of linear operators. More precisely, well-known notions like
$G$-convergence, $H$-convergence as well as the recent notion of nonlocal
$H$-convergence are discussed and characterised by certain convergence
statements under the weak operator topology. Having introduced and described
these notions predominantly made for static or variational type problems, we
further study these convergences in the context of dynamic equations like the
heat equation, the wave equation or Maxwell's equations. The survey is intended
to clarify the ideas and highlight the operator theoretic aspects of
homogenisation theory in the autonomous case.

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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int