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

A strong compactness result in the spirit of the Lions-Aubin-Simon lemma is proven for piecewise constant functions in time (uτ ) 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 uτ − uτ (· − τ) instead of all time shifts uτ − uτ (· − h) for h > 0, as required in Simon’s compactness theorem. This simplifies significantly the application of the Rothe method in the existence analysis of parabolic problems.