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

By M. Dreher, A. Jungel. 2012

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Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species (2016, methodology): “In view of (27) and (29), we can apply the AubinLions lemma in the version of [13], which yields the existence of a subsequence, which is not relabeled, such that, as (τ, ε) → 0, u ) → u strongly in L(2)(QT ) and almost everywhere, (30) u ) ⇀ u weakly in L2(0, T ; H1( )), (31) εw → 0 strongly in L2(”
A Note on Aubin-Lions-Dubinskiĭ Lemmas (2013, methodology): “This result generalizes slightly Theorem 1 in [10] and Theorem 3 in [8] (for piecewise constant functions in time).”
The boundedness-by-entropy method for cross-diffusion systems (2015, methodology): “e that the result would follow from the Aubin compactness lemma if yτ was bounded from below by a positive constant, since in this situation, it would suﬃce to apply the Aubin lemma in the version of [25] to infer the strong convergence of (a subsequence of) (zτ) in L2(0,T;L2(Ω)) which, together wit”