Acta Applicandae Mathematicae

, Volume 133, Issue 1, pp 33–43

A Note on Aubin-Lions-Dubinskiĭ Lemmas

Authors

    • School of SciencesBeijing University of Posts and Telecommunications
    • Institute for Analysis and Scientific ComputingVienna University of Technology
  • Ansgar Jüngel
    • Institute for Analysis and Scientific ComputingVienna University of Technology
  • Jian-Guo Liu
    • Department of Physics and Department of MathematicsDuke University
Article

DOI: 10.1007/s10440-013-9858-8

Cite this article as:
Chen, X., Jüngel, A. & Liu, J. Acta Appl Math (2014) 133: 33. doi:10.1007/s10440-013-9858-8

Abstract

Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskiĭ lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinskiĭ (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.

Keywords

Compactness in Banach spacesRothe methodDubinskii lemmaSeminormed cone

Mathematics Subject Classification (2000)

46B5035A35

Copyright information

© Springer Science+Business Media Dordrecht 2013