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arXiv · 2610.04478

On some concepts of convergence and their connections

Tatiana Danielsson·Liselott Flodén·Anders Holmbom·Pernilla Johnsen·Marianne Olsson Lindberg·Jens Persson
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Abstract

The notions of classical two-scale convergence and the periodic unfolding method, which both rely on an additional scale for the representation of periodic micro-oscillations, are in this paper traced back to the wider concept of general two-scale convergence. Moreover, a comparison is made between very weak two-scale convergence and periodic unfolding with respect to sequences bounded in Sobolev spaces, amplified by the scale of the micro-oscillations. It turns out that, for amplified sequences, these approaches are not equivalent in an immediate sense. The paper both serves as a literature overview, with examples and illustrations of the concepts of convergence, and contains new results.

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Tatiana Danielsson, Liselott Flodén, Anders Holmbom, Pernilla Johnsen, Marianne Olsson Lindberg, Jens Persson. 2026-10-03. On some concepts of convergence and their connections. https://arxiv.org/abs/2610.04478

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