A note on Aubin-Lions-Dubinskiǐ Lemmas
Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskiǐ lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinskiǐ (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. © 2013 Springer Science+Business Media.
Chen, X; Jüngel, A; Liu, JG
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