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

Michael Dreher, Ansgar Juengel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Citations (Scopus)


A strong compactness result in the spirit of the Lions-Aubin-Simon lemma is proven for piecewise constant functions in time (u(tau)) 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(tau) - u(tau) (center dot - tau) instead of all time shifts u(tau) - u(tau) (center dot - 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. (C) 2011 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)3072-3077
Number of pages6
JournalNonlinear Analysis: Theory, Methods and Applications
Issue number6
Publication statusPublished - Apr 2012


  • Compactness
  • Aubin lemma
  • Rothe method


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