Acta Applicandae Mathematicae

, Volume 133, Issue 1, pp 33–43

A Note on Aubin-Lions-Dubinskiĭ Lemmas

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

Authors and Affiliations

  1. 1.School of SciencesBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyWienAustria
  3. 3.Department of Physics and Department of MathematicsDuke UniversityDurhamUSA