[Back]

X. Chen, A. Jüngel, J. Liu:
"A note on Aubin-Lions-Dubinskii lemmas";
in: "ASC Report 14/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 11.

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 (1965) for eminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and Jüngel (2012) and Chen and Liu (2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations.

Compactness in Banach spaces, Rothe method, Dubinskii lemma, seminormed cone.

http://www.asc.tuwien.ac.at/preprint/2013/asc14x2013.pdf