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X. Chen, A. Jüngel, J. Liu:
"A Note on Aubin-Lions-Dubinskiı Lemmas";
Acta Applicandae Mathematicae, 133 (2014), 33 - 43.

Strong compactness results for families of functions in seminormed nonnegative
cones in the spirit of the Aubin-Lions-Dubinski˘ı lemma are proven, refining some recent
results in the literature. The first theorem sharpens slightly a result of Dubinski˘ı (in Mat.
Sb. 67(109):609-642, 1965) for seminormed cones. The second theorem applies to piecewise
constant functions in time and sharpens slightly the results of Dreher and Jüngel (in
Nonlinear Anal. 75:3072-3077, 2012) and Chen and Liu (in Appl. Math. Lett. 25:2252-
2257, 2012). An application is given, which is useful in the study of porous-medium or
fast-diffusion type equations.

Siehe englisches Abstract.

Compactness in Banach spaces;· Rothe method

http://dx.doi.org/10.1007/s10440-013-9858-8