COMPACT FAMILIES OF PIECEWISE CONSTANT FUNCTIONS IN Lp(0, T;B)

Abstract. 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. 1