M. Dreher, A. Jüngel:

"Compact families of piecewise constant functions in Lp(0,T;B)";

in: "ASC Report 26/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

A strong compactness result in the spirit of the Lions-Aubin-Simon lemma is

proven for piecewise constant functions in time (u ) with values in a Banach space. The

main feature of our result is that it is sufficient to verify one uniform estimate for the time

shifts u (t)−u (t− ) instead of all time shifts u (t)−u (t−h) for h > 0, as required in

Simonīs compactness theorem. This simplifies significantly the application of the Rothe

method in the existence analysis of parabolic problems.

http://www.asc.tuwien.ac.at/preprint/2011/asc26x2011.pdf

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